Existence and Uniqueness Result for Fuzzy Fractional Order Goursat Partial Differential Equations
Date
2024
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Article
Publisher
Multidisciplinary Digital Publishing Institute (MDPI)
Journal Title
Existence and Uniqueness Result for Fuzzy Fractional Order Goursat Partial Differential Equations
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Abstract
In 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.
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Fractal and Fractional