Abstract
The current study is devoted to investigating the existence and uniqueness of solutions for a new class of symmetrically coupled system of nonlinear hyperbolic partial-fractional differential equations in generalized Banach spaces in the sense of ψ–Caputo partial fractional derivative. Our approach is based on the Krasnoselskii-type fixed point theorem in generalized Banach spaces and Perov’s fixed point theorem together with the Bielecki norm, while Urs’s approach was used to prove the Ulam–Hyers stability of solutions of our system. Finally, some examples are provided in order to illustrate our theoretical results.
Highlights
During the last twenty years, fractional differential equations have gained considerable attention in various fields of applied mathematics and engineering
A generalization of derivatives of both Caputo and Caputo–Hadamard was provided by Almeida in [10]. He named it as a ψ–Caputo fractional derivative
We present some basic definitions and classical results about fractional calculus, matrix analysis, and fixed-point theorems that are be used throughout this paper
Summary
During the last twenty years, fractional differential equations have gained considerable attention in various fields of applied mathematics and engineering. For some recent results on the existence and stability of solutions for a coupled system of fractional differential equations involving different forms of fractional derivatives, we refer the reader to [23,24,25,26,27,28]. Reason, in this paper, we study the existence, uniqueness, and the Ulam–Hyers stability of solutions for the following coupled system with symmetry: (
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
