Browsing by Author "Noor Jamal"

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    Existence and Uniqueness Result for Fuzzy Fractional Order Goursat Partial Differential Equations
    (Multidisciplinary Digital Publishing Institute (MDPI), 2024) Muhammad Sarwar; Noor Jamal; Kamaleldin Abodayeh; Chanon Promsakon; Thanin Sitthiwirattham; M. 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
    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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    Existence of solution for fractional differential equations involving symmetric fuzzy numbers
    (American Institute of Mathematical Sciences, 2024) Muhammad Sarwar; Noor Jamal; Kamaleldin Abodayeh; Manel Hleili; Thanin Sitthiwirattham; Chanon Promsakon; M. Sarwar; Department of Mathematics, Univdersity of malakand, Dir Lower, Pakistan; email: sarwarswati@gmail.com; C. Promsakon; Department of Mathematics, Faculty of Applied Science, King MongkutÕs University of Technology North Bangkok, Bangkok, 10800, Thailand; email: chanon.p@sci.kmutnb.ac.th
    Linear correlated fractional fuzzy differential equations (LCFFDEs) are one of the best tools for dealing with physical problems with uncertainty. The LCFFDEs mostly do not have unique solutions, especially if the basic fuzzy number is symmetric. The LCFFDEs of symmetric basic fuzzy numbers extend to the new system by extension and produce many solutions. The existing literature does not have any criteria to ensure the existence of unique solutions to LCFFDEs. In this study, we will explore the main causes of the extension and the unavailability of unique solutions. Next, we will discuss the existence and uniqueness conditions of LCFFDEs by using the concept of metric fixed point theory. For the useability of established results, we will also provide numerical examples and discuss their unique solutions. To show the authenticity of the solutions, we will also provide 2D and 3D plots of the solutions. © 2024 the Author(s), licensee AIMS Press.