{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T18:13:06Z","timestamp":1782929586980,"version":"3.54.5"},"reference-count":77,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2021,7]]},"DOI":"10.1007\/s00366-019-00913-y","type":"journal-article","created":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T15:02:46Z","timestamp":1577890966000},"page":"1751-1764","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Numerical solution of the fractional Rayleigh\u2013Stokes model arising in a heated generalized second-grade fluid"],"prefix":"10.1007","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3041-8726","authenticated-orcid":false,"given":"O.","family":"Nikan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2047-5081","authenticated-orcid":false,"given":"A.","family":"Golbabai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-4879","authenticated-orcid":false,"given":"J. A. Tenreiro","family":"Machado","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9704-2893","authenticated-orcid":false,"given":"T.","family":"Nikazad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,1,1]]},"reference":[{"key":"913_CR1","first-page":"1","volume":"20","author":"M Abbaszadeh","year":"2019","unstructured":"Abbaszadeh M, Dehghan M (2019) Meshless upwind local radial basis function-finite difference technique to simulate the time-fractional distributed-order advection-diffusion equation. Eng Comput 20:1\u201317","journal-title":"Eng Comput"},{"issue":"6","key":"913_CR2","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1016\/0020-7462(95)00035-6","volume":"30","author":"R Bandelli","year":"1995","unstructured":"Bandelli R, Rajagopal K (1995) Start-up flows of second grade fluids in domains with one finite dimension. Int J Non-Linear Mech 30(6):817\u2013839","journal-title":"Int J Non-Linear Mech"},{"key":"913_CR3","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511543241","volume-title":"Radial basis functions: theory and implementations","author":"MD Buhmann","year":"2003","unstructured":"Buhmann MD (2003) Radial basis functions: theory and implementations, vol 12. Cambridge University Press, Cambridge"},{"issue":"1","key":"913_CR4","first-page":"340","volume":"204","author":"CM Chen","year":"2008","unstructured":"Chen CM, Liu F, Anh V (2008) Numerical analysis of the Rayleigh\u2013Stokes problem for a heated generalized second grade fluid with fractional derivatives. Appl Math Comput 204(1):340\u2013351","journal-title":"Appl Math Comput"},{"key":"913_CR5","volume-title":"A course in approximation theory","author":"EW Cheney","year":"2009","unstructured":"Cheney EW, Light WA (2009) A course in approximation theory, vol 101. American Mathematical Society, New York"},{"key":"913_CR6","unstructured":"Chenoweth ME (2012) A local radial basis function method for the numerical solution of partial differential equations"},{"issue":"3","key":"913_CR7","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s00366-016-0491-9","volume":"33","author":"M Dehghan","year":"2017","unstructured":"Dehghan M, Abbaszadeh M (2017) A finite element method for the numerical solution of Rayleigh\u2013Stokes problem for a heated generalized second grade fluid with fractional derivatives. Eng Comput 33(3):587\u2013605","journal-title":"Eng Comput"},{"key":"913_CR8","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.enganabound.2014.09.008","volume":"50","author":"M Dehghan","year":"2015","unstructured":"Dehghan M, Abbaszadeh M, Mohebbi A (2015) An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein\u2013Gordon equations. Eng Anal Bound Elem 50:412\u2013434","journal-title":"Eng Anal Bound Elem"},{"issue":"2","key":"913_CR9","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s11075-016-0103-1","volume":"73","author":"M Dehghan","year":"2016","unstructured":"Dehghan M, Abbaszadeh M, Mohebbi A (2016) Analysis of a meshless method for the time fractional diffusion-wave equation. Numerical Algorithms 73(2):445\u2013476","journal-title":"Numerical Algorithms"},{"key":"913_CR10","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.cpc.2017.03.012","volume":"217","author":"M Dehghan","year":"2017","unstructured":"Dehghan M, Mohammadi V (2017) A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schr\u00f6dinger equations using an explicit time discretization: Runge-Kutta method. Comput Phys Commun 217:23\u201334","journal-title":"Comput Phys Commun"},{"issue":"3\u20135","key":"913_CR11","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/S0898-1221(01)00295-4","volume":"43","author":"TA Driscoll","year":"2002","unstructured":"Driscoll TA, Fornberg B (2002) Interpolation in the limit of increasingly flat radial basis functions. Comput Math Appl 43(3\u20135):413\u2013422","journal-title":"Comput Math Appl"},{"key":"913_CR12","doi-asserted-by":"crossref","DOI":"10.1142\/6437","volume-title":"Meshfree approximation methods with matlab: (With CD-ROM)","author":"GE Fasshauer","year":"2007","unstructured":"Fasshauer GE (2007) Meshfree approximation methods with matlab: (With CD-ROM), vol 6. World Scientific Publishing Company, Singapore"},{"issue":"1\u20132","key":"913_CR13","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/BF01178551","volume":"150","author":"C Fetec\u0103u","year":"2001","unstructured":"Fetec\u0103u C, Zierep J (2001) On a class of exact solutions of the equations of motion of a second grade fluid. Acta Mech 150(1\u20132):135\u2013138","journal-title":"Acta Mech"},{"issue":"2","key":"913_CR14","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1137\/09076756X","volume":"33","author":"B Fornberg","year":"2011","unstructured":"Fornberg B, Larsson E, Flyer N (2011) Stable computations with Gaussian radial basis functions. SIAM J Sci Comput 33(2):869\u2013892","journal-title":"SIAM J Sci Comput"},{"issue":"4","key":"913_CR15","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1016\/j.camwa.2012.11.006","volume":"65","author":"B Fornberg","year":"2013","unstructured":"Fornberg B, Lehto E, Powell C (2013) Stable calculation of Gaussian-based RBF-FD stencils. Comput Math Appl 65(4):627\u2013637","journal-title":"Comput Math Appl"},{"issue":"1","key":"913_CR16","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1137\/060671991","volume":"30","author":"B Fornberg","year":"2007","unstructured":"Fornberg B, Piret C (2007) A stable algorithm for flat radial basis functions on a sphere. SIAM J Sci Comput 30(1):60\u201380","journal-title":"SIAM J Sci Comput"},{"issue":"3","key":"913_CR17","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/j.camwa.2007.01.028","volume":"54","author":"B Fornberg","year":"2007","unstructured":"Fornberg B, Zuev J (2007) The Runge phenomenon and spatially variable shape parameters in RBF interpolation. Comput Math Appl 54(3):379\u2013398","journal-title":"Comput Math Appl"},{"issue":"4","key":"913_CR18","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1023\/A:1018916902176","volume":"8","author":"C Franke","year":"1998","unstructured":"Franke C, Schaback R (1998) Convergence order estimates of meshless collocation methods using radial basis functions. Adv Comput Math 8(4):381\u2013399","journal-title":"Adv Comput Math"},{"issue":"157","key":"913_CR19","first-page":"181","volume":"38","author":"R Franke","year":"1982","unstructured":"Franke R (1982) Scattered data interpolation: tests of some methods. Math Comput 38(157):181\u2013200","journal-title":"Math Comput"},{"key":"913_CR20","doi-asserted-by":"crossref","unstructured":"Fu ZJ (2016) Radial basis function methods for fractional derivative applications. In: ASME 2015 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers Digital Collection","DOI":"10.1115\/DETC2015-48016"},{"issue":"10","key":"913_CR21","doi-asserted-by":"crossref","first-page":"1651","DOI":"10.1016\/j.camwa.2009.03.038","volume":"57","author":"A Golbabai","year":"2009","unstructured":"Golbabai A, Mammadov M, Seifollahi S (2009) Solving a system of nonlinear integral equations by an RBF network. Comput Math Appl 57(10):1651\u20131658","journal-title":"Comput Math Appl"},{"issue":"2","key":"913_CR22","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1007\/s40314-014-0132-0","volume":"34","author":"A Golbabai","year":"2015","unstructured":"Golbabai A, Mohebianfar E, Rabiei H (2015) On the new variable shape parameter strategies for radial basis functions. Comput Appl Math 34(2):691\u2013704","journal-title":"Comput Appl Math"},{"key":"913_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10614-019-09880-4","volume":"1","author":"A Golbabai","year":"2019","unstructured":"Golbabai A, Nikan O (2019) A computational method based on the moving least-squares approach for pricing double barrier options in a time-fractional Black-Scholes model. Comput Econ 1:1\u201323. https:\/\/doi.org\/10.1007\/s10614-019-09880-4","journal-title":"Comput Econ"},{"issue":"4","key":"913_CR24","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s40314-019-0957-7","volume":"38","author":"A Golbabai","year":"2019","unstructured":"Golbabai A, Nikan O, Nikazad T (2019) Numerical analysis of time fractional Black\u2013Scholes European option pricing model arising in financial market. Comput Appl Math 38(4):173","journal-title":"Comput Appl Math"},{"issue":"11","key":"913_CR25","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1016\/j.enganabound.2012.04.001","volume":"36","author":"A Golbabai","year":"2012","unstructured":"Golbabai A, Rabiei H (2012) A meshfree method based on radial basis functions for the eigenvalues of transient stokes equations. Eng Anal Bound Elem 36(11):1555\u20131559","journal-title":"Eng Anal Bound Elem"},{"issue":"2","key":"913_CR26","first-page":"877","volume":"174","author":"A Golbabai","year":"2006","unstructured":"Golbabai A, Seifollahi S (2006) Numerical solution of the second kind integral equations using radial basis function networks. Appl Math Comput 174(2):877\u2013883","journal-title":"Appl Math Comput"},{"key":"913_CR27","first-page":"1","volume":"20","author":"S Haq","year":"2019","unstructured":"Haq S, Hussain M, Ghafoor A (2019) A computational study of variable coefficients fractional advection-diffusion-reaction equations via implicit meshless spectral algorithm. Eng Comput 20:1\u201321","journal-title":"Eng Comput"},{"issue":"8","key":"913_CR28","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1029\/JB076i008p01905","volume":"76","author":"RL Hardy","year":"1971","unstructured":"Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76(8):1905\u20131915","journal-title":"J Geophys Res"},{"issue":"8\u20139","key":"913_CR29","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0898-1221(90)90272-L","volume":"19","author":"RL Hardy","year":"1990","unstructured":"Hardy RL (1990) Theory and applications of the multiquadric\u2013biharmonic method 20 years of discovery 1968\u20131988. Comput Math Appl 19(8\u20139):163\u2013208","journal-title":"Comput Math Appl"},{"key":"913_CR30","first-page":"1","volume":"20","author":"H Hassani","year":"2019","unstructured":"Hassani H, Avazzadeh Z, Machado JT (2019) Numerical approach for solving variable-order space-time fractional telegraph equation using transcendental bernstein series. Eng Comput 20:1\u201312","journal-title":"Eng Comput"},{"issue":"12","key":"913_CR31","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0898-1221(92)90174-G","volume":"24","author":"E Kansa","year":"1992","unstructured":"Kansa E, Carlson R (1992) Improved accuracy of multiquadric interpolation using variable shape parameters. Comput Math Appl 24(12):99\u2013120","journal-title":"Comput Math Appl"},{"issue":"7\u20138","key":"913_CR32","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0898-1221(00)00071-7","volume":"39","author":"E Kansa","year":"2000","unstructured":"Kansa E, Hon Y (2000) Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations. Comput Math Appl 39(7\u20138):123\u2013138","journal-title":"Comput Math Appl"},{"issue":"8\u20139","key":"913_CR33","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0898-1221(90)90270-T","volume":"19","author":"EJ Kansa","year":"1990","unstructured":"Kansa EJ (1990) Multiquadrics\u2014a scattered data approximation scheme with applications to computational fluid-dynamics-I surface approximations and partial derivative estimates. Comput Math Appl 19(8\u20139):127\u2013145","journal-title":"Comput Math Appl"},{"issue":"8\u20139","key":"913_CR34","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0898-1221(90)90271-K","volume":"19","author":"EJ Kansa","year":"1990","unstructured":"Kansa EJ (1990) Multiquadrics\u2014a scattered data approximation scheme with applications to computational fluid-dynamics-II solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput Math Appl 19(8\u20139):147\u2013161","journal-title":"Comput Math Appl"},{"issue":"7","key":"913_CR35","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1016\/j.enganabound.2009.02.008","volume":"33","author":"EJ Kansa","year":"2009","unstructured":"Kansa EJ, Aldredge RC, Ling L (2009) Numerical simulation of two-dimensional combustion using mesh-free methods. Eng Anal Bound Elem 33(7):940\u2013950","journal-title":"Eng Anal Bound Elem"},{"key":"913_CR36","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1016\/j.ijheatmasstransfer.2017.11.011","volume":"118","author":"N Li","year":"2018","unstructured":"Li N, Su H, Gui D, Feng X (2018) Multiquadric RBF-FD method for the convection-dominated diffusion problems base on Shishkin nodes. Int J Heat Mass Transf 118:734\u2013745","journal-title":"Int J Heat Mass Transf"},{"issue":"1","key":"913_CR37","first-page":"12","volume":"191","author":"F Liu","year":"2007","unstructured":"Liu F, Zhuang P, Anh V, Turner I, Burrage K (2007) Stability and convergence of the difference methods for the space-time fractional advection\u2013diffusion equation. Appl Math Comput 191(1):12\u201320","journal-title":"Appl Math Comput"},{"issue":"3","key":"913_CR38","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1016\/j.cnsns.2010.05.027","volume":"16","author":"JT Machado","year":"2011","unstructured":"Machado JT, Kiryakova V, Mainardi F (2011) Recent history of fractional calculus. Commun Nonlinear Sci Numer Simul 16(3):1140\u20131153","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"189","key":"913_CR39","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1090\/S0025-5718-1990-0993931-7","volume":"54","author":"W Madych","year":"1990","unstructured":"Madych W, Nelson S (1990) Multivariate interpolation and conditionally positive definite functions. ii. Math Comput 54(189):211\u2013230","journal-title":"Math Comput"},{"key":"913_CR40","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/978-94-009-6466-2_7","volume-title":"Approximation theory and spline functions","author":"CA Micchelli","year":"1984","unstructured":"Micchelli CA (1984) Interpolation of scattered data: distance matrices and conditionally positive definite functions. Approximation theory and spline functions. Springer, Berlin, pp 143\u2013145"},{"key":"913_CR41","first-page":"1","volume":"20","author":"F Mirzaee","year":"2019","unstructured":"Mirzaee F, Samadyar N (2019) Combination of finite difference method and meshless method based on radial basis functions to solve fractional stochastic advection-diffusion equations. Eng Comput 20:1\u201314","journal-title":"Eng Comput"},{"key":"913_CR42","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.cma.2013.05.012","volume":"264","author":"A Mohebbi","year":"2013","unstructured":"Mohebbi A, Abbaszadeh M, Dehghan M (2013) Compact finite difference scheme and RBF meshless approach for solving 2D Rayleigh\u2013Stokes problem for a heated generalized second grade fluid with fractional derivatives. Comput Methods Appl Mech Eng 264:163\u2013177","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"7","key":"913_CR43","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1140\/epjp\/i2019-12748-1","volume":"134","author":"O Nikan","year":"2019","unstructured":"Nikan O, Golbabai A, Nikazad T (2019) Solitary wave solution of the nonlinear KdV-Benjamin\u2013Bona\u2013Mahony\u2013Burgers model via two meshless methods. Eur Phys J Plus 134(7):367","journal-title":"Eur Phys J Plus"},{"issue":"4","key":"913_CR44","doi-asserted-by":"crossref","first-page":"2757","DOI":"10.1007\/s11071-019-05160-w","volume":"97","author":"O Nikan","year":"2019","unstructured":"Nikan O, Machado JT, Golbabai A, Nikazad T (2019) Numerical investigation of the nonlinear modified anomalous diffusion process. Nonlinear Dyn 97(4):2757\u20132775","journal-title":"Nonlinear Dyn"},{"key":"913_CR45","unstructured":"Oldham KB, Spanier J (1974) The fractional calculus, vol. 111 of mathematics in science and engineering"},{"issue":"1","key":"913_CR46","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s00366-018-0584-8","volume":"35","author":"\u00d6 Oru\u00e7","year":"2019","unstructured":"Oru\u00e7 \u00d6, Esen A, Bulut F (2019) A haar wavelet approximation for two-dimensional time fractional reaction\u2013subdiffusion equation. Eng Comput 35(1):75\u201386","journal-title":"Eng Comput"},{"key":"913_CR47","volume-title":"Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications","author":"I Podlubny","year":"1998","unstructured":"Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, vol 198. Elsevier, Oxford"},{"key":"913_CR48","first-page":"144","volume":"339","author":"H Pourbashash","year":"2018","unstructured":"Pourbashash H, Oshagh MKe (2018) Local RBF-FD technique for solving the two-dimensional modified anomalous sub-diffusion equation. Appl Math Comput 339:144\u2013152","journal-title":"Appl Math Comput"},{"issue":"4","key":"913_CR49","doi-asserted-by":"crossref","first-page":"1431","DOI":"10.1007\/s00366-018-0673-8","volume":"35","author":"K Rabiei","year":"2019","unstructured":"Rabiei K, Ordokhani Y (2019) Solving fractional pantograph delay differential equations via fractional-order boubaker polynomials. Eng Comput 35(4):1431\u20131441","journal-title":"Eng Comput"},{"issue":"5\u20136","key":"913_CR50","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/0020-7462(82)90006-3","volume":"17","author":"K Rajagopal","year":"1982","unstructured":"Rajagopal K (1982) A note on unsteady unidirectional flows of a non-Newtonian fluid. Int J Non-Linear Mech 17(5\u20136):369\u2013373","journal-title":"Int J Non-Linear Mech"},{"issue":"5","key":"913_CR51","doi-asserted-by":"crossref","first-page":"1831","DOI":"10.1016\/j.camwa.2017.12.007","volume":"75","author":"J Rashidinia","year":"2018","unstructured":"Rashidinia J, Khasi M, Fasshauer G (2018) A stable Gaussian radial basis function method for solving nonlinear unsteady convection\u2013diffusion\u2013reaction equations. Comput Math Appl 75(5):1831\u20131850","journal-title":"Comput Math Appl"},{"key":"913_CR52","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.wavemoti.2019.05.006","volume":"90","author":"J Rashidinia","year":"2019","unstructured":"Rashidinia J, Rasoulizadeh MN (2019) Numerical methods based on radial basis function-generated finite difference (RBF-FD) for solution of GKdVB equation. Wave Motion 90:152\u2013167","journal-title":"Wave Motion"},{"key":"913_CR53","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4020-6042-7","volume-title":"Advances in fractional calculus","author":"J Sabatier","year":"2007","unstructured":"Sabatier J, Agrawal OP, Machado JT (2007) Advances in fractional calculus, vol 4. Springer, Berlin"},{"issue":"19","key":"913_CR54","first-page":"9853","volume":"218","author":"SA Sarra","year":"2012","unstructured":"Sarra SA (2012) A local radial basis function method for advection\u2013diffusion\u2013reaction equations on complexly shaped domains. Appl Math Comput 218(19):9853\u20139865","journal-title":"Appl Math Comput"},{"key":"913_CR55","first-page":"2","volume":"2","author":"SA Sarra","year":"2009","unstructured":"Sarra SA, Kansa EJ (2009) Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations. Adv Comput Mech 2:2","journal-title":"Adv Comput Mech"},{"issue":"11","key":"913_CR56","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1016\/j.enganabound.2009.07.003","volume":"33","author":"SA Sarra","year":"2009","unstructured":"Sarra SA, Sturgill D (2009) A random variable shape parameter strategy for radial basis function approximation methods. Eng Anal Bound Elem 33(11):1239\u20131245","journal-title":"Eng Anal Bound Elem"},{"issue":"3","key":"913_CR57","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/BF02432002","volume":"3","author":"R Schaback","year":"1995","unstructured":"Schaback R (1995) Error estimates and condition numbers for radial basis function interpolation. Adv Comput Math 3(3):251\u2013264","journal-title":"Adv Comput Math"},{"issue":"5","key":"913_CR58","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.1016\/j.nonrwa.2005.09.007","volume":"7","author":"F Shen","year":"2006","unstructured":"Shen F, Tan W, Zhao Y, Masuoka T (2006) The Rayleigh\u2013Stokes problem for a heated generalized second grade fluid with fractional derivative model. Nonlinear Anal Real World Appl 7(5):1072\u20131080","journal-title":"Nonlinear Anal Real World Appl"},{"issue":"1","key":"913_CR59","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s00366-017-0522-1","volume":"34","author":"E Shivanian","year":"2018","unstructured":"Shivanian E, Jafarabadi A (2018) Rayleigh\u2013Stokes roblem for a heated generalized second grade fluid with fractional derivatives: a stable scheme based on spectral meshless radial point interpolation. Eng Comput 34(1):77\u201390","journal-title":"Eng Comput"},{"issue":"7\u20138","key":"913_CR60","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1016\/S0045-7825(02)00618-7","volume":"192","author":"C Shu","year":"2003","unstructured":"Shu C, Ding H, Yeo K (2003) Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier\u2013Stokes equations. Comput Methods Appl Mech Eng 192(7\u20138):941\u2013954","journal-title":"Comput Methods Appl Mech Eng"},{"key":"913_CR61","unstructured":"Sturgill DJ (2009) Variable shape parameter strategies in radial basis funchtion methods. Ph.D. thesis, Marshall University Libraries"},{"issue":"4","key":"913_CR62","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.ijnonlinmec.2004.07.016","volume":"40","author":"W Tan","year":"2005","unstructured":"Tan W, Masuoka T (2005) Stokes\u2019 first problem for a second grade fluid in a porous half-space with heated boundary. Int J Non-Linear Mech 40(4):515\u2013522","journal-title":"Int J Non-Linear Mech"},{"issue":"1\u20132","key":"913_CR63","first-page":"102","volume":"26","author":"JA Tenreiro Machado","year":"2019","unstructured":"Tenreiro Machado JA, Lopes AM (2019) Fractional-order kinematic analysis of biomechanical inspired manipulators. J Vib Control 26(1\u20132):102\u2013111","journal-title":"J Vib Control"},{"issue":"1","key":"913_CR64","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s00466-003-0501-9","volume":"33","author":"A Tolstykh","year":"2003","unstructured":"Tolstykh A, Shirobokov D (2003) On using radial basis functions in a \u201cfinite difference mode\u201d with applications to elasticity problems. Comput Mech 33(1):68\u201379","journal-title":"Comput Mech"},{"key":"913_CR65","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511617539","volume-title":"Scattered data approximation","author":"H Wendland","year":"2004","unstructured":"Wendland H (2004) Scattered data approximation, vol 17. Cambridge University Press, Cambridge"},{"issue":"1","key":"913_CR66","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.jcp.2005.05.030","volume":"212","author":"GB Wright","year":"2006","unstructured":"Wright GB, Fornberg B (2006) Scattered node compact finite difference-type formulas generated from radial basis functions. J Comput Phys 212(1):99\u2013123","journal-title":"J Comput Phys"},{"issue":"1","key":"913_CR67","first-page":"45","volume":"19","author":"XJ Yang","year":"2018","unstructured":"Yang XJ (2018) New rheological problems involving general fractional derivatives with nonsingular power-law kernels. Proc Roman Acad Ser A Math Phys Tech Sci Inf Sci 19(1):45\u201352","journal-title":"Proc Roman Acad Ser A Math Phys Tech Sci Inf Sci"},{"key":"913_CR68","doi-asserted-by":"crossref","DOI":"10.1201\/9780429284083","volume-title":"General fractional derivatives: theory, methods and applications","author":"XJ Yang","year":"2019","unstructured":"Yang XJ (2019) General fractional derivatives: theory, methods and applications. Chapman and Hall, New York"},{"issue":"6B","key":"913_CR69","doi-asserted-by":"crossref","first-page":"3751","DOI":"10.2298\/TSCI180921260Y","volume":"23","author":"XJ Yang","year":"2019","unstructured":"Yang XJ (2019) New general calculi with respect to another functions applied to describe the Newton-like dashpot models in anomalous. Therm Sci 23(6B):3751\u20133757","journal-title":"Therm Sci"},{"issue":"6B","key":"913_CR70","doi-asserted-by":"crossref","first-page":"4117","DOI":"10.2298\/TSCI191028427Y","volume":"23","author":"XJ Yang","year":"2019","unstructured":"Yang XJ (2019) New non-conventional methods for quantitative concepts of anomalous rheology. Therm Sci 23(6B):4117\u20134127","journal-title":"Therm Sci"},{"issue":"3A","key":"913_CR71","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.2298\/TSCI190220277Y","volume":"23","author":"XJ Yang","year":"2019","unstructured":"Yang XJ, Gao F, Jing HW (2019) New mathematical models in anomalous viscoelasticity from the derivative with respect to another function view point. Therm Sci 23(3A):1555\u20131561","journal-title":"Therm Sci"},{"issue":"04","key":"913_CR72","doi-asserted-by":"crossref","first-page":"1740002","DOI":"10.1142\/S0218348X17400023","volume":"25","author":"XJ Yang","year":"2017","unstructured":"Yang XJ, Gao F, Srivastava H (2017) Non-differentiable exact solutions for the nonlinear ODEs defined on fractal sets. Fractals 25(04):1740002","journal-title":"Fractals"},{"issue":"18","key":"913_CR73","doi-asserted-by":"crossref","first-page":"7539","DOI":"10.1002\/mma.5904","volume":"42","author":"XJ Yang","year":"2019","unstructured":"Yang XJ, Machado JT (2019) A new fractal nonlinear Burger\u2019s equation arising in the acoustic signals propagation. Math Methods Appl Sci 42(18):7539\u20137544","journal-title":"Math Methods Appl Sci"},{"issue":"1","key":"913_CR74","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.jcp.2005.12.006","volume":"216","author":"SB Yuste","year":"2006","unstructured":"Yuste SB (2006) Weighted average finite difference methods for fractional diffusion equations. J Comput Phys 216(1):264\u2013274","journal-title":"J Comput Phys"},{"issue":"17","key":"913_CR75","doi-asserted-by":"crossref","first-page":"8345","DOI":"10.1002\/mma.5222","volume":"41","author":"Y Zhou","year":"2018","unstructured":"Zhou Y, Peng L, Huang Y (2018) Duhamel\u2019s formula for time-fractional Schr\u00f6dinger equations. Math Methods Appl Sci 41(17):8345\u20138349","journal-title":"Math Methods Appl Sci"},{"issue":"12","key":"913_CR76","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1007\/s10483-009-1205-7","volume":"30","author":"P Zhuang","year":"2009","unstructured":"Zhuang P, Liu Q (2009) Numerical method of Rayleigh\u2013Stokes problem for heated generalized second grade fluid with fractional derivative. Appl Math Mech 30(12):1533","journal-title":"Appl Math Mech"},{"issue":"2\u20138","key":"913_CR77","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/j.ijengsci.2007.04.015","volume":"45","author":"J Zierep","year":"2007","unstructured":"Zierep J, Fetecau C (2007) Energetic balance for the Rayleigh\u2013Stokes problem of a Maxwell fluid. Int J Eng Sci 45(2\u20138):617\u2013627","journal-title":"Int J Eng Sci"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-019-00913-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-019-00913-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-019-00913-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,6]],"date-time":"2021-07-06T17:08:39Z","timestamp":1625591319000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-019-00913-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,1]]},"references-count":77,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,7]]}},"alternative-id":["913"],"URL":"https:\/\/doi.org\/10.1007\/s00366-019-00913-y","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,1]]},"assertion":[{"value":"7 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 December 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 January 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}