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Access Right: info:eu-repo/semantics/closedAccessSubject: Fractional Differential Equations

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    Existence, Uniqueness and Successive Approximations for (λ, Ψ)-Hilfer Fractional Differential Equations
    (Univ Politehnica Bucharest, Sci Bull, 2024) Krim, Salim; Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, Erdal
    The focus of this paper is on investigating a particular type of nonlinear (lambda, psi)-Hilfer fractional differential equations, and analyzing their existence results. Our approach involves utilizing Banach's fixed point theorem, and we also explore the global convergence of successive approximations to provide additional insights into the topic. To further illustrate our findings, we provide some examples that supplement our main results.
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    Citation - WoS: 146
    Citation - Scopus: 157
    On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions
    (Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Aksoy, Umit; Aksoy, Ümit; Karapinar, Erdal; Karapınar, Erdal; Erhan, Inci M.; Erhan, İnci; Sevinik Adıgüzel, Rezan; Aksoy, Ümit; Karapınar, Erdal; Erhan, İnci; Mathematics; Mathematics; Mathematics
    The aim of this article is twofold. Firstly, to study fixed points of mappings on b metric spaces satisfying a general contractive condition called Geraghty type hybrid contraction. Secondly, to apply the theoretical results to the problem of existence and uniqueness of solutions of boundary value problems with integral boundary conditions associated with a certain type of nonlinear fractional differential equations. The conditions for the existence of fixed points for Geraghty type hybrid contractions are determined and several consequences of the main results are deduced. Some examples on boundary value problems for nonlinear fractional differential equations of order 3 < alpha <= 4 are provided, where the existence and uniqueness of solutions are shown by using Geraghty type contractions.