Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Jarad, FahdSubject: search.filters.subject.Existence

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Now showing 1 - 7 of 7
  • Article
    Citation - Scopus: 1
    Study of Impulsive Problem with Caputo Fractional Derivative Involving Nonlocal Conditions Using Fixed Point Theory
    (Kyungnam University Press, 2025) Dhandapani, Swathi; Umapathi, Karthik Raja; Mathuraiveeran, Jeyaraman; Shah, Kamal; Abdeljawad (Maraaba) T., Thabet; Jarad, Fahd; Abdeljawad, Thabet
    In this article, we study the existence of solutions for an impulsive Caupto fractional differential equations with a class of initial value problem dependence on the Lipschitz first derivative conditions. Our main tool is a Banach's fixed point theorem and Leray-Schauder fixed point theorem. We also investigate the existence of fractional Derivative with non-local conditions. An numerical example is given to clarify the results. © 2025 Elsevier B.V., All rights reserved.
  • Article
    On Solutions of Variable-Order Fractional Differential Equations
    (Elsevier B.V., 2017) Akgül, Ali; Inc, Mustafa; Baleanu, Dumitru; Abdalla, Bahaaeldin; Jarad, Fahd; Bouchelaghem, Faycal; Abdeljawad, Thabet; Ardjouni, Abdelouaheb; Boulares, Hamid; Shah, Kamal
    Numerical calculation of the fractional integrals and derivatives is the code tosearch fractional calculus and solve fractional differential equations. The exactsolutions to fractional differential equations are compelling to get in real ap-plications, due to the nonlocality and complexity of the fractional differentialoperators, especially for variable-order fractional differential equations. There-fore, it is significant to enhance numerical methods for fractional differentialequations. In this work, we consider variable-order fractional differential equa-tions by reproducing kernel method. There has been much attention in theuse of reproducing kernels for the solutions to many problems in the recentyears. We give an example to demonstrate how efficiently our theory can beimplemented in practice.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    New Results for a Coupled System of Abr Fractional Differential Equations With Sub-Strip Boundary Conditions
    (Amer inst Mathematical Sciences-aims, 2022) Panchal, Satish K.; Aljaaidi, Tariq A.; Jarad, Fahd; Almalahi, Mohammed A.
    In this article, we investigate sufficient conditions for the existence, uniqueness and UlamHyers (UH) stability of solutions to a new system of nonlinear ABR fractional derivative of order 1 < e <= 2 subjected to multi-point sub-strip boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of Leray-Schauder alternative theorem and Banach's contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam-Hyers (UH). Finally, we provide one example in order to show the validity of our results.
  • Article
    Citation - WoS: 56
    Citation - Scopus: 67
    On Hilfer Generalized Proportional Fractional Derivative
    (Springer, 2020) Kumam, Poom; Jarad, Fahd; Borisut, Piyachat; Jirakitpuwapat, Wachirapong; Ahmed, Idris
    Motivated by the Hilfer and the Hilfer-Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann-Liouville and Caputo generalized proportional fractional derivative. Some important properties of the proposed derivative are presented. Based on the proposed derivative, we consider a nonlinear fractional differential equation with nonlocal initial condition and show that this equation is equivalent to the Volterra integral equation. In addition, the existence and uniqueness of solutions are proven using fixed point theorems. Furthermore, we offer two examples to clarify the results.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 18
    On Existence-Uniqueness Results for Proportional Fractional Differential Equations and Incomplete Gamma Functions
    (Springer, 2020) Jarad, Fahd; Laadjal, Zaid; Abdeljawad, Thabet
    In this article, we employ the lower regularized incomplete gamma functions to demonstrate the existence and uniqueness of solutions for fractional differential equations involving nonlocal fractional derivatives (GPF derivatives) generated by proportional derivatives of the form D-rho=(1-rho)+rho D, rho is an element of[0,1], (1) where D is the ordinary differential operator.
  • Article
    Citation - WoS: 46
    Citation - Scopus: 47
    Existence of Mild Solutions To Hilfer Fractional Evolution Equations in Banach Space
    (Springer Basel Ag, 2020) Abdeljawad, Thabet; Sousa, J. Vanterler da C.; Jarad, Fahd
    In this paper, we investigate the existence of mild solutions to semilinear evolution fractional differential equations with non-instantaneous impulses, using the concepts of equicontinuous (alpha,beta)-resolvent operator function P-alpha,P-beta(t) and Kuratowski measure of non-compactness in Banach space Omega.
  • Article
    Citation - WoS: 34
    Citation - Scopus: 35
    Existence and Stability Results To a Class of Fractional Random Implicit Differential Equations Involving a Generalized Hilfer Fractional Derivative
    (Amer inst Mathematical Sciences-aims, 2020) Harikrishnan, Sugumaran; Shah, Kamal; Kanagarajan, Kuppusamy; Jarad, Fahd
    In this paper, the existence, uniqueness and stability of random implicit fractional differential equations (RIFDs) with nonlocal condition and impulsive effect involving a generalized Hilfer fractional derivative (HFD) are discussed. The arguments are discussed via Krasnoselskii's fixed point theorems, Schaefer's fixed point theorems, Banach contraction principle and Ulam type stability. Some examples are included to ensure the abstract results.