HuiYan Cheng, Naila, Akbar Zada, Ioan-Lucian Popa, Afef Kallekh
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引用次数: 0
Abstract
The primary objective of this manuscript is to investigate the existence and uniqueness of solutions for the Langevin $(\mathtt{k},\varphi )$ -Hilfer fractional differential equation of different orders with multipoint nonlocal fractional integral boundary conditions. We consider the generalized version of the Hilfer fractional diferential equation called as $(\mathtt{k},\varphi )$ -Hilfer fractional differential equation. We provide some significant outcomes about $(\mathtt{k},\varphi )$ -Hilfer fractional Langevin differential equation that requires deriving equivalent fractional integral equation to $(\mathtt{k},\varphi )$ -Hilfer Langevin fractional differential equation. The existence result is established using the Krasnoselskii’s fixed-point theorem, while the uniqueness is addressed with the help of Banach contraction principle. Additionally, we investigate the different forms of Ulam stability for the solution of the mentioned problem, under specific conditions. To validate our main outcomes, we present a detailed example at the end of the manuscript.
期刊介绍:
The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.