On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative

Year 2023, Volume: 6 Issue: 3, 122 - 129, 30.09.2023

Samira Zerbib Khalid Hilal Ahmed Kajounı

https://doi.org/10.32323/ujma.1288015

Abstract

This work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order $ 0 < \theta < 1 $ in an arbitrary Banach space. We rely on some arguments to present the mild solution to our problem in terms of an $ \theta $-resolvent family. Then we study the existence of this mild solution by using Krasnoselskii's fixed point theorem. Finally, we give an example to prove our results.

Keywords

Atangana-Baleanu-Caputo derivative, Fractional semi-linear differential equation, Krasnoselskii fixed point theorem, Resolvent family

Supporting Institution

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