Semi-analytical solutions for fuzzy caputoÐfabrizio fractional-order two-dimensional heat equation

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dc.contributor.authorThanin Sitthiwirattham
dc.contributor.authorMuhammad Arfan
dc.contributor.authorKamal Shah
dc.contributor.authorAnwar Zeb
dc.contributor.authorSalih Djilali
dc.contributor.authorSaowaluck Chasreechai
dc.contributor.correspondenceA. Zeb; Department of Mathematics, Abbotabad Campus, COMSATS University of Islamabad, Khyber Pakhtunkhwa, 22060, Pakistan; email: anwar@cuiatd.edu.pk
dc.date.accessioned2025-03-10T07:35:28Z
dc.date.available2025-03-10T07:35:28Z
dc.date.issued2021
dc.description.abstractIn the analysis in this article, we developed a scheme for the computation of a semi-analytical solution to a fuzzy fractional-order heat equation of two dimensions having some external diffusion source term. For this, we applied the Laplace transform along with decomposition tech-niques and the Adomian polynomial under the CaputoÐFabrizio fractional differential operator. Furthermore, for obtaining a semi-analytical series-type solution, the decomposition of the unknown quantity and its addition established the said solution. The obtained series solution was calculated and approached the approximate solution of the proposed equation. For the validation of our scheme, three different examples have been provided, and the solutions were calculated in fuzzy form. All the three illustrations simulated two different fractional orders between 0 and 1 for the upper and lower portions of the fuzzy solution. The said fractional operator is nonsingular and global due to the presence of the exponential function. It globalizes the dynamical behavior of the said equation, which is guaranteed for all types of fuzzy solution lying between 0 and 1 at any fractional order. The fuzziness is also included in the unknown quantity due to the fuzzy number providing the solution in fuzzy form, having upper and lower branches. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
dc.identifier.citationFractal and Fractional
dc.identifier.doi10.3390/fractalfract5040139
dc.identifier.issn25043110
dc.identifier.scopus2-s2.0-85116477062
dc.identifier.urihttps://repository.dusit.ac.th//handle/123456789/4690
dc.languageEnglish
dc.publisherMDPI
dc.rightsAll Open Access; Gold Open Access
dc.rights.holderScopus
dc.subject2D-fractional fuzzy heat equation
dc.subjectCaputoÐFabrizio fractional operator
dc.subjectSemi-analytical solution
dc.titleSemi-analytical solutions for fuzzy caputoÐfabrizio fractional-order two-dimensional heat equation
dc.typeArticle
mods.location.urlhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85116477062&doi=10.3390%2ffractalfract5040139&partnerID=40&md5=be4486cb7f48c5419fb80fd8513718a4
oaire.citation.issue4
oaire.citation.volume5
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