is paper deals with the existence of mild solutions for the following Cauchy problem:where d α (.)/dt α is the so-called conformable fractional derivative. e linear part A is the infinitesimal generator of a uniformly continuous semigroup (T(t)) t≥0 on a Banach space X, f and g are given functions. e main result is proved by using the Darbo-Sadovskii fixed point theorem without assuming the compactness of the family (T(t)) t>0 and the Lipshitz condition on the nonlocal part g.

We study in this paper, the existence results for initial value problems for hybrid fractional integro-differential equations. By using fixed point theorems for the sum of three operators are used for proving the main results.An example is also given to demonstrate the applications of our main results.

In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. Some concrete applications to partial differential equations are considered. Some concrete applications to partial differential equations are considered.

In this paper, a class of nondense impulsive differential equations with nonlocal condition in the frame of the conformable fractional derivative is studied. The abstract results concerning the existence, uniqueness and stability of the integral solution are obtained by using the extrapolation semigroup approach combined with some fixed point theorems.

The study of coupled systems of hybrid fractional differential equations requires the attention of scientists for the exploration of their different important aspects. Our aim in this paper is to study the existence and uniqueness of the solution for impulsive hybrid fractional differential equations. The novelty of this work is the study of a coupled system of impulsive hybrid fractional differential equations with initial and boundary hybrid conditions. We used the classical fixed-point theorems such as the Banach fixed-point theorem and Leray–Schauder alternative fixed-point theorem for existence results. We also give an example of the main results.