{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:06:41Z","timestamp":1760242001784,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,3]],"date-time":"2018-12-03T00:00:00Z","timestamp":1543795200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007345","name":"King Mongkut's University of Technology North Bangkok","doi-asserted-by":"publisher","award":["KMUTNB-60-ART-062"],"award-info":[{"award-number":["KMUTNB-60-ART-062"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper studies the existence and uniqueness of solutions for a new coupled system of nonlinear sequential Caputo and Hadamard fractional differential equations with coupled separated boundary conditions, which include as special cases the well-known symmetric boundary conditions. Banach\u2019s contraction principle, Leray\u2013Schauder\u2019s alternative, and Krasnoselskii\u2019s fixed-point theorem were used to derive the desired results, which are well-illustrated with examples.<\/jats:p>","DOI":"10.3390\/sym10120701","type":"journal-article","created":{"date-parts":[[2018,12,3]],"date-time":"2018-12-03T06:02:09Z","timestamp":1543816929000},"page":"701","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Coupled Systems of Sequential Caputo and Hadamard Fractional Differential Equations with Coupled Separated Boundary Conditions"],"prefix":"10.3390","volume":"10","author":[{"given":"Suphawat","family":"Asawasamrit","sequence":"first","affiliation":[{"name":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"},{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8185-3539","authenticated-orcid":false,"given":"Jessada","family":"Tariboon","sequence":"additional","affiliation":[{"name":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6216-1593","authenticated-orcid":false,"given":"Woraphak","family":"Nithiarayaphaks","sequence":"additional","affiliation":[{"name":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1115\/1.3167615","article-title":"On the appearance of the fractional derivative in the behavior of real materials","volume":"51","author":"Torvik","year":"1984","journal-title":"J. Appl. Mech."},{"key":"ref_2","unstructured":"Magin, R.L. (2006). Fractional Calculus in Bioengineering, Begell House Publishers."},{"key":"ref_3","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier Science B.V.. North-Holland Mathematics Studies, 204."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Klafter, J., Lim, S.C., and Metzler, R. (2011). Fractional Dynamics in Physics, World Scientific.","DOI":"10.1142\/9789814340595"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1007\/s40435-016-0224-3","article-title":"A delay fractional order model for the co-infection of malaria and HIV\/AIDS","volume":"5","author":"Carvalho","year":"2017","journal-title":"Int. J. Dyn. Control"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ahmad, B., Alsaedi, A., Ntouyas, S.K., and Tariboon, J. (2017). Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities, Springer.","DOI":"10.1007\/978-3-319-52141-1"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/s11071-012-0714-6","article-title":"LMI-based stabilization of a class of fractional-order chaotic systems","volume":"72","author":"Faieghi","year":"2013","journal-title":"Nonlinear Dyn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"20120155","DOI":"10.1098\/rsta.2012.0155","article-title":"Chaos synchronization in fractional differential systems","volume":"371","author":"Zhang","year":"2013","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0370-1573(00)00070-3","article-title":"The random walk\u2019s guide to anomalous diffu sion: a fractional dynamics approach","volume":"339","author":"Metzler","year":"2000","journal-title":"Phys. Rep."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.ecolmodel.2015.06.016","article-title":"Dynamic analysis of time fractional order phytoplankton-toxic phytoplankton\u2013 zooplankton system","volume":"318","author":"Javidi","year":"2015","journal-title":"Ecol. Model."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1515\/fca-2015-0024","article-title":"On a system of fractional differential equations with coupled integral boundary conditions","volume":"18","author":"Henderson","year":"2015","journal-title":"Fract. Calc. Appl. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3322","DOI":"10.1002\/mma.3298","article-title":"Analysis of fractional order differential coupled systems","volume":"38","author":"Wang","year":"2015","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.2298\/FIL1705331Z","article-title":"Monotone iterative method for a class of nonlinear fractional differential equations on unbounded domains in Banach spaces","volume":"31","author":"Zhang","year":"2017","journal-title":"Filomat"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"202","DOI":"10.25103\/jestr.085.25","article-title":"Higher order and fractional diffusive equations","volume":"8","author":"Assante","year":"2015","journal-title":"J. Eng. Sci. Technol. Rev."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1515\/math-2015-0079","article-title":"System of fractional differential equations with Erd\u00e9lyi-Kober fractional integral conditions","volume":"13","author":"Thongsalee","year":"2015","journal-title":"Open Math."},{"key":"ref_16","first-page":"3","article-title":"On a coupled system of sequential fractional differential equations with variable coeffcients and coupled integral boundary conditions","volume":"60","author":"Ahmad","year":"2017","journal-title":"Bull. Math. Soc. Sci. Math. Roum."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1515\/math-2017-0057","article-title":"Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain","volume":"15","author":"Tariboon","year":"2017","journal-title":"Open Math."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.chaos.2017.08.035","article-title":"Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions","volume":"104","author":"Ahmad","year":"2017","journal-title":"Chaos Solitons Fractals"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Tariboon, J., Cuntavepanit, A., Ntouyas, S.K., and Nithiarayaphaks, W. (2018). Separated boundary value problems of sequential Caputo and Hadamard fractional differential equations. J. Funct. Spaces, 2018.","DOI":"10.1155\/2018\/6974046"},{"key":"ref_20","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Academic Press."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1186\/1687-1847-2012-142","article-title":"Caputo-type modification of the Hadamard fractional derivatives","volume":"2012","author":"Jarad","year":"2012","journal-title":"Adv. Differ. Equ."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Granas, A., and Dugundji, J. (2003). Fixed Point Theory, Springer.","DOI":"10.1007\/978-0-387-21593-8"},{"key":"ref_23","first-page":"123","article-title":"Two remarks on the method of successive approximations","volume":"10","author":"Krasnoselskii","year":"1955","journal-title":"Uspekhi Mat. Nauk"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/12\/701\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:30:43Z","timestamp":1760196643000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/12\/701"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,3]]},"references-count":23,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["sym10120701"],"URL":"https:\/\/doi.org\/10.3390\/sym10120701","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,12,3]]}}}