{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:09:33Z","timestamp":1765544973864,"version":"3.38.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,11,16]],"date-time":"2024-11-16T00:00:00Z","timestamp":1731715200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,11,16]],"date-time":"2024-11-16T00:00:00Z","timestamp":1731715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,2]]},"DOI":"10.1007\/s40314-024-02991-1","type":"journal-article","created":{"date-parts":[[2024,11,16]],"date-time":"2024-11-16T12:30:43Z","timestamp":1731760243000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Symmetry analysis of the time fractional potential-KdV equation"],"prefix":"10.1007","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8148-171X","authenticated-orcid":false,"given":"B. El","family":"Ansari","sequence":"first","affiliation":[]},{"given":"E. H.","family":"El Kinani","sequence":"additional","affiliation":[]},{"given":"A.","family":"Ouhadan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,11,16]]},"reference":[{"key":"2991_CR1","doi-asserted-by":"publisher","first-page":"1155","DOI":"10.3934\/math.2022068","volume":"7","author":"M Aslam","year":"2022","unstructured":"Aslam M et al (2022) Fractal fractional derivative on chemistry kinetics hires problem. AIMS Math 7:1155\u20131184","journal-title":"AIMS Math"},{"key":"2991_CR2","doi-asserted-by":"crossref","DOI":"10.1142\/8180","volume-title":"Fractional calculus: models and numerical methods","author":"D Baleanu","year":"2012","unstructured":"Baleanu D, Diethelm K, Scalas E, Trujillo JJ (2012) Fractional calculus: models and numerical methods, vol 3. World Scientific, Singapore"},{"key":"2991_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40314-021-01456-z","volume":"40","author":"LC Barros","year":"2021","unstructured":"Barros LC et al (2021) The memory effect on fractional calculus: an application in the spread of covid-19. Comput Appl Math 40:1\u201321","journal-title":"Comput Appl Math"},{"key":"2991_CR4","volume-title":"Symmetries and differential equations","author":"GW Bluman","year":"2013","unstructured":"Bluman GW, Kumei S (2013) Symmetries and differential equations, vol 81. Springer, Berlin"},{"key":"2991_CR5","doi-asserted-by":"publisher","first-page":"2050010","DOI":"10.1142\/S0219887820500103","volume":"17","author":"Y Chatibi","year":"2020","unstructured":"Chatibi Y, El Kinani EH, Ouhadan A (2020) Lie symmetry analysis and conservation laws for the time fractional Black\u2013Scholes equation. Int J Geom Methods Mod Phys 17:2050010","journal-title":"Int J Geom Methods Mod Phys"},{"key":"2991_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20545-3","volume-title":"Functional fractional calculus","author":"S Das","year":"2011","unstructured":"Das S (2011) Functional fractional calculus, vol 1. Springer, Berlin"},{"key":"2991_CR7","doi-asserted-by":"publisher","first-page":"3413","DOI":"10.1155\/S0161171203301486","volume":"2003","author":"L Debnath","year":"2003","unstructured":"Debnath L et al (2003) Recent applications of fractional calculus to science and engineering. Int J Math Math Sci 2003:3413\u20133442","journal-title":"Int J Math Math Sci"},{"key":"2991_CR8","doi-asserted-by":"publisher","first-page":"1560075","DOI":"10.1142\/S2010194515600757","volume":"38","author":"E El Kinani","year":"2015","unstructured":"El Kinani E, Ouhadan A (2015) Lie symmetry analysis of some time fractional partial differential equations. Int J Mod Phys Conf Ser 38:1560075\u20131560083","journal-title":"Int J Mod Phys Conf Ser"},{"key":"2991_CR9","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1016\/j.camwa.2013.05.006","volume":"66","author":"RK Gazizov","year":"2013","unstructured":"Gazizov RK, Kasatkin AA (2013) Construction of exact solutions for fractional order differential equations by the invariant subspace method. Comput Math Appl 66:576\u2013584","journal-title":"Comput Math Appl"},{"key":"2991_CR10","first-page":"21","volume":"9","author":"RK Gazizov","year":"2007","unstructured":"Gazizov RK, Kasatkin A, Lukashchuk SY (2007) Continuous transformation groups of fractional differential equations. Vestnik Usatu 9:21","journal-title":"Vestnik Usatu"},{"key":"2991_CR11","doi-asserted-by":"crossref","unstructured":"Hassouna M, El Kinani EH, Ouhadan A (2022) Fractional calculus: Applications in rheology, Fractional Order Systems : An Overview of Mathematics, Design, and Applications for Engineers vol.1 : 513\u2013549 Academic Press","DOI":"10.1016\/B978-0-12-824293-3.00018-1"},{"key":"2991_CR12","first-page":"73","volume":"135","author":"J-H He","year":"2003","unstructured":"He J-H (2003) Homotopy perturbation method: a new nonlinear analytical technique. Appl Math Comput 135:73\u201379","journal-title":"Appl Math Comput"},{"key":"2991_CR13","doi-asserted-by":"publisher","DOI":"10.1142\/8072","volume-title":"Fractional calculus: an introduction for physicists","author":"R Herrmann","year":"2011","unstructured":"Herrmann R (2011) Fractional calculus: an introduction for physicists. World Scientific, Singapore"},{"key":"2991_CR14","doi-asserted-by":"publisher","DOI":"10.1142\/3779","volume-title":"Applications of fractional calculus in physics","author":"R Hilfer","year":"2000","unstructured":"Hilfer R (2000) Applications of fractional calculus in physics. World scientific, Singapore"},{"key":"2991_CR15","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/j.jmaa.2006.10.078","volume":"333","author":"NH Ibragimov","year":"2007","unstructured":"Ibragimov NH (2007) A new conservation theorem. J Math Anal Appl 333:311\u2013328","journal-title":"J Math Anal Appl"},{"key":"2991_CR16","first-page":"422","volume":"38","author":"M Inc","year":"2022","unstructured":"Inc M, Ic \u00dc, Inan \u0130E, Gom\u00e9z-Aguilar JF (2022) Generalized-expansion method for some soliton wave solutions of burgers-like and potential kdv equations. Numer Methods Partial Differ Equ 38:422\u2013433","journal-title":"Numer Methods Partial Differ Equ"},{"key":"2991_CR17","doi-asserted-by":"publisher","DOI":"10.1142\/p926","volume-title":"Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models","author":"F Mainardi","year":"2022","unstructured":"Mainardi F (2022) Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models. World Scientific, Singapore"},{"key":"2991_CR18","volume-title":"An introduction to the fractional calculus and fractional differential equations","author":"KS Miller","year":"1993","unstructured":"Miller KS, Ross B (1993) An introduction to the fractional calculus and fractional differential equations. Wiley, Hoboken"},{"key":"2991_CR19","unstructured":"Noether E (1971) Invariante variationsprobleme. nachr. vd ges. d. wiss. zu g\u00f6ttingen (1918) 235; e. noether e ma tavel. Transport Theor Stat Phys 1:183"},{"key":"2991_CR20","volume-title":"The fractional calculus theory and applications of differentiation and integration to arbitrary order","author":"K Oldham","year":"1974","unstructured":"Oldham K, Spanier J (1974) The fractional calculus theory and applications of differentiation and integration to arbitrary order. Elsevier, Amsterdam"},{"key":"2991_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4350-2","volume-title":"Applications of Lie groups to differential equations","author":"PJ Olver","year":"1993","unstructured":"Olver PJ (1993) Applications of Lie groups to differential equations, vol 107. Springer, Berlin"},{"key":"2991_CR22","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. Elsevier, Amsterdam"},{"key":"2991_CR23","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/s40314-023-02186-0","volume":"42","author":"M Rahioui","year":"2023","unstructured":"Rahioui M, El Kinani EH, Ouhadan A (2023) Lie symmetry analysis and conservation laws for the time fractional generalized advection-diffusion equation. Comput Appl Math 42:50","journal-title":"Comput Appl Math"},{"key":"2991_CR24","volume-title":"Principles of mathematical analysis","author":"W Rudin","year":"1953","unstructured":"Rudin W (1953) Principles of mathematical analysis. McGraw-Hill, New York"},{"key":"2991_CR25","unstructured":"Samko SG (1993) Fractional Integrals and Derivatives : Theory and Applications. Gordon and Breach Science Publishers, Switzerland, Langhorne, PA, USA"},{"key":"2991_CR26","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1051\/mmnp\/2018072","volume":"14","author":"F Song","year":"2019","unstructured":"Song F, Yu Z, Yang H (2019) Modeling and analysis of fractional neutral disturbance waves in arterial vessels. Math Model Nat Phenom 14:301","journal-title":"Math Model Nat Phenom"},{"key":"2991_CR27","volume-title":"Fractional dynamics: applications of fractional calculus to dynamics of particles, fields and media","author":"VE Tarasov","year":"2011","unstructured":"Tarasov VE (2011) Fractional dynamics: applications of fractional calculus to dynamics of particles, fields and media. Springer, Berlin"},{"key":"2991_CR28","doi-asserted-by":"publisher","first-page":"4163","DOI":"10.1016\/j.cnsns.2011.01.014","volume":"16","author":"M ur Rehman","year":"2011","unstructured":"ur Rehman M, Khan RA (2011) The legendre wavelet method for solving fractional differential equations. Commun Nonlinear Sci Numer Simul 16:4163\u20134173","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"2991_CR29","doi-asserted-by":"publisher","first-page":"1059","DOI":"10.1007\/s11071-013-1189-9","volume":"76","author":"G-W Wang","year":"2014","unstructured":"Wang G-W et al (2014) Singular solitons, shock waves, and other solutions to potential kdv equation. Nonlinear Dyn 76:1059\u20131068","journal-title":"Nonlinear Dyn"},{"key":"2991_CR30","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.chaos.2006.06.018","volume":"36","author":"A-M Wazwaz","year":"2008","unstructured":"Wazwaz A-M (2008) Analytic study on the one and two spatial dimensional potential kdv equations. Chaos Solitons Fractals 36:175\u2013181","journal-title":"Chaos Solitons Fractals"},{"key":"2991_CR31","doi-asserted-by":"publisher","first-page":"2050040","DOI":"10.1142\/S0219887820500401","volume":"17","author":"M Yourdkhany","year":"2020","unstructured":"Yourdkhany M, Nadjafikhah M, Toomanian M (2020) Lie symmetry analysis, conservation laws and some exact solutions of the time-fractional buckmaster equation. Int J Geom Methods Mod Phys 17:2050040","journal-title":"Int J Geom Methods Mod Phys"},{"key":"2991_CR32","volume-title":"Hamiltonian chaos and fractional dynamics","author":"GM Zaslavsky","year":"2005","unstructured":"Zaslavsky GM (2005) Hamiltonian chaos and fractional dynamics. Oxford University Press, New York"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02991-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-024-02991-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02991-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T05:16:26Z","timestamp":1741065386000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-024-02991-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,16]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["2991"],"URL":"https:\/\/doi.org\/10.1007\/s40314-024-02991-1","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2024,11,16]]},"assertion":[{"value":"30 October 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 November 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"34"}}