Open AccessQualitative Analyses of ψ-Caputo Type Fractional Integrodifferential Equations in Banach Spaces
Author(s) -
Mohammed S. Abdo
Publication year - 2022
Publication title -
journal of advances in applied and computational mathematics
Language(s) - English
Resource type - Journals
ISSN - 2409-5761
DOI - 10.15377/2409-5761.2022.09.1
Subject(s) - mathematics , fixed point theorem , fractional calculus , uniqueness , banach space , banach fixed point theorem , picard–lindelöf theorem , class (philosophy) , type (biology) , pure mathematics , mathematical analysis , nonlinear system , physics , ecology , quantum mechanics , artificial intelligence , computer science , biology
In this research paper, we develop and extend some qualitative analyses of a class of a nonlinear fractional integro-differential equation involving ψ-Caputo fractional derivative (ψ-CFD) and ψ-Riemann-Liouville fractional integral (ψ-RLFI). The existence and uniqueness theorems are obtained in Banach spaces via an equivalent fractional integral equation with the help of Banach’s fixed point theorem (B’sFPT) and Schaefer’s fixed point theorem (S’sFPT). An example explaining the main results is also constructed.