Abstract
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.
Highlights
Fractional differential equations have gained popularity due to their applications in many domains of science and engineering [1–3]
Many studies and discussion related to conformable fractional derivative have appeared in several areas of applications [1–10]
One of the main novelties of this paper is the concept on a mild solution for system (1). en, using some fixed point theorems such as Banach contraction mapping principle and Schauder’s fixed point theorem, we derive many existence and uniqueness results concerning the mild solution for system (1) under the different assumptions on the nonlinear terms
Summary
Fractional differential equations have gained popularity due to their applications in many domains of science and engineering [1–3]. Many studies and discussion related to conformable fractional derivative have appeared in several areas of applications [1–10]. Motivated by the abovementioned works, we consider the following impulsive differential equation with conformable fractional derivative:. En, using some fixed point theorems such as Banach contraction mapping principle and Schauder’s fixed point theorem, we derive many existence and uniqueness results concerning the mild solution for system (1) under the different assumptions on the nonlinear terms. We discuss, a nonlocal impulsive differential equation with conformable fractional derivative. We adopt the ideas given in [14–16] and obtained some new existence and uniqueness results for system (2) under the different assumptions on the nonlocal terms. Some interesting examples are presented to illustrate the theory
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