Existence and Uniqueness Result for Fuzzy Fractional Order Goursat Partial Differential Equations

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dc.contributor.authorMuhammad Sarwar
dc.contributor.authorNoor Jamal
dc.contributor.authorKamaleldin Abodayeh
dc.contributor.authorChanon Promsakon
dc.contributor.authorThanin Sitthiwirattham
dc.contributor.correspondenceM. Sarwar; Department of Mathematics, University of Malakand, Chakdara, Dir(L) Khyber Pakhtunkhwa, 18000, Pakistan; email: sarwar@uom.edu.pk; C. Promsakon; Department of Mathematics, Faculty of Applied Science, King MongkutÕs University of Technology North, Bangkok, 10800, Thailand; email: chanon.p@sci.kmutnb.ac.th
dc.date.accessioned2025-03-10T07:34:20Z
dc.date.available2025-03-10T07:34:20Z
dc.date.issued2024
dc.description.abstractIn this manuscript, we discuss fractional fuzzy Goursat problems with CaputoÕs (Formula presented.) -differentiability. The second-order mixed derivative term in Goursat problems and two types of CaputoÕs (Formula presented.) -differentiability pose challenges to dealing with Goursat problems. Therefore, in this study, we convert Goursat problems to equivalent systems fuzzy integral equations to deal properly with the mixed derivative term and two types of CaputoÕs (Formula presented.) -differentiability. In this study, we utilize the concept of metric fixed point theory to discuss the existence of a unique solution of fractional fuzzy Goursat problems. For the useability of established theoretical work, we provide some numerical problems. We also discuss the solutions to numerical problems by conformable double Laplace transform. To show the validity of the solutions we provide 3D plots. We discuss, as an application, why fractional partial fuzzy differential equations are the generalization of usual partial fuzzy differential equations by providing a suitable reason. Moreover, we show the advantages of the proposed fractional transform over the usual Laplace transform. © 2024 by the authors.
dc.identifier.citationFractal and Fractional
dc.identifier.doi10.3390/fractalfract8050250
dc.identifier.issn25043110
dc.identifier.scopus2-s2.0-85194276467
dc.identifier.urihttps://repository.dusit.ac.th//handle/123456789/4468
dc.languageEnglish
dc.publisherMultidisciplinary Digital Publishing Institute (MDPI)
dc.rights.holderScopus
dc.subjectfuzzy number
dc.subjectgH-differentiability
dc.subjectGoursat problem
dc.subjectmixed derivative term
dc.subjectuncertainty
dc.titleExistence and Uniqueness Result for Fuzzy Fractional Order Goursat Partial Differential Equations
dc.typeArticle
mods.location.urlhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85194276467&doi=10.3390%2ffractalfract8050250&partnerID=40&md5=6b9caae90898110bfd0ff6070e48daec
oaire.citation.issue5
oaire.citation.volume8
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