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

Authors : Samira Zerbib, Khalid Hilal, Ahmed Kajouni

Pages : 122-129

Doi:10.32323/ujma.1288015

View : 26 | Download : 11

Publication Date : 2023-09-30

Article Type : Research

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