Some theorems on fractional semilinear evolution equations

Abstract

In this paper, we investigate the existence, uniqueness and other properties of solutions of fractional semilinear evolution equations in Banach spaces. The results are obtained by using fractional calculus, the well-known Banach fixed point theorem coupled with Bielecki type norm and the integral inequality established by E. Hernandez.

Existence and data dependence results for fractional differential equations involving atangana-baleanu derivative

“…Inspired by the work of [ 42 – 44 ], on the line of [ 40 , 41 ], we consider multi-derivative nonlinear FDEs involving Riemann-Liouville version of AB-fractional derivative (ABR derivative) of the from: where , , denotes the ABR-fractional differential operator of order and is a non-linear function.…”

On nonlinear mixed fractional integro-differential equations with positive constant coefficient

“…In [38], by using Banach fixed point theorem coupled with Bielecki type norm and the integral inequality, Tidke investigated the existence, uniqueness and other properties of solutions of fractional semilinear evolution equation of the type:…”