Abstract
In this paper, we study the solution of impulsive fractional differential equations with multiple delays by using the nonlinear alternative of Leray–Schauder and the Banach fixed point method. Also, we prove that the equations have at least one solution or unique solution with certain conditions. In the last part, we give two examples to illustrate the usefulness of the main results.
Highlights
With the development of fractional calculus and the requirement for field applications of physics, mathematics, and chemical engineering, fractional differential equations have attracted great interest in recent years.Based on the nonlinear alternative of a Leray–Schauder model, we have considered and cited previous studies on the existence of solutions of fractional differential equations for investigating the existence and uniqueness of fractional functional equations
5 Conclusions In this paper, we use the nonlinear alternative of Leray–Schauder and the Banach fixed point theorem to prove the existence and uniqueness of solution for the fractional order impulsive functional differential equations with multiple delays
Summary
With the development of fractional calculus and the requirement for field applications of physics, mathematics, and chemical engineering, fractional differential equations have attracted great interest in recent years (see, for example, [1–8]).Based on the nonlinear alternative of a Leray–Schauder model, we have considered and cited previous studies on the existence of solutions of fractional differential equations for investigating the existence and uniqueness of fractional functional equations. Zhou et al have already used Krasnoselskii’s fixed point theory to study the existence and uniqueness of fractional function equations [9, 10]. Some researchers have studied fractional order impulsive differential equations and discussed the existence solution of nonlinear functional differential equations with multiple delays [11, 12].
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