Abstract
In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed.
Highlights
Introduction and PreliminariesFractional calculus is a generalization of classical differentiation and integration to an arbitrary real order
For the basic theory of fractional calculus and fractional differential equations we refer to the monographs [1,2,3,4,5,6,7,8] and references therein
Non-instantaneous impulsive differential equation was introduced by Hernández and O’Regan in [20] pointed out that the instantaneous impulses cannot characterize some processes such as evolution processes in pharmacotherapy
Summary
Introduction and PreliminariesFractional calculus is a generalization of classical differentiation and integration to an arbitrary real order. M, (1) is reduced to a non impulsive fractional boundary value problem. Existence and uniqueness results are established for the the non-instantaneous impulsive Riemann– Stieltjes fractional integral boundary value problem (1) by using classical fixed point theorems.
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