Browsing by Author "Muhammad Sarwar"

Now showing 1 - 6 of 6
  • Default Image
    Item
    _-Contraction of HardyÐRogers type in supermetric spaces with applications
    (Springer Nature, 2024) Kamaleldin Abodayeh; Syed Khayyam Shah; Muhammad Sarwar; Varaporn Wattanakejorn; Thanin Sitthiwirattham; S.K. Shah; Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, 18800, Pakistan; email: khayyamshah0@gmail.com; V. Wattanakejorn; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: varaporn_wat@dusit.ac.th
    This article focuses on studying some fixed-point results via _-contraction of HardyÐRogers type in the context of supermetric space and ordered supermetric space. We also introduced rational-type z-contraction on supermetric space. For authenticity, some illustrative examples and applications have been included. © The Author(s) 2024.
  • Default Image
    Item
    Controllability of Hilfer fractional neutral impulsive stochastic delayed differential equations with nonlocal conditions
    (Elsevier Ltd, 2024) Sadam Hussain; Muhammad Sarwar; Kamaleldin Abodayeh; Chanon Promsakon; Thanin Sitthiwirattham; M. Sarwar; Department of Mathematics, University of Malakand, Dir Lower, Pakistan; email: sarwar@uom.edu.pk; C. Promsakon; Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand; email: chanon.p@sci.kmutnb.ac.th
    In this paper, the controllability for Hilfer fractional neutral stochastic differential equations with infinite delay and nonlocal conditions has been investigated. Using concepts from fractional calculus, semigroup of operators, fixed-point theory, measures of noncompactness, and stochastic theory the main controllability conclusion is attained. The applications of the key findings are finally illustrated with two examples. © 2024 The Author(s)
  • Default Image
    Item
    Controllability of semilinear noninstantaneous impulsive neutral stochastic differential equations via Atangana-Baleanu Caputo fractional derivative
    (Elsevier B.V., 2024) Muhammad Sarwar; Sadam Hussain; Kamaleldin Abodayeh; Sawitree Moonsuwan; Thanin Sitthiwirattham; M. Sarwar; Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, 18000, Pakistan; email: sarwarswati@gmail.com; S. Moonsuwan; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: sawitree_moo@dusit.ac.th
    This study mainly concerns the controllability of semilinear noninstantaneous impulsive neutral stochastic differential equations via the Atangana-Baleanu (AB) Caputo fractional derivative (FD). The essential findings are created using methods and concepts from semigroup theory, stochastic theory, fractional calculus, K-set contraction, and measure of noncompactness. Finally, an example is provided to demonstrate the applications of the key findings. © 2024 The Author(s)
  • Default Image
    Item
    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.
  • Default Image
    Item
    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.
  • Default Image
    Item
    _iri_-type generalized F-contractions with integral inclusion in super metric spaces
    (Elsevier B.V., 2024) Kamaleldin Abodayeh; Syed Khayyam Shah; Muhammad Sarwar; Chanon Promsakon; Thanin Sitthiwirattham; S. Khayyam Shah; Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, 18800, Pakistan; email: Khayyamshah0@gmail.com
    This study aims to explore _iri_-type generalized F-contractions, almost F-contractions, and the combination of these contractions in the framework of super metric spaces. These generalizations are significant because they hold where the usual metric conditions mayn't be fulfilled. Using the iteration method, fixed point results have been obtained for these contractions, and through examples and applications to integral inclusions and contractions, we extend existing literature significantly. This extension offers new insights and demonstrates practical relevance. © 2024 The Author(s)