On Fractional Integro-differential Equations with State-Dependent Delay and Non-Instantaneous Impulses

Abstract

In this paper, we prove the existence of mild solution of the fractional integro-differential equations with state-dependent delay with not instantaneous impulses. The existence results are obtained under the conditions in respect of Kuratowski's measure of noncompactness. An example is also given to illustrate the results. RESUMENEn este artículo, demostramos la existencia de soluciones mild de ecuaciones integrodiferenciales fraccionarias con retardo dependiente del estado e impulsos no instantáneos. Los resultados de existencia se obtienen bajo condiciones respecto de la medida de Kuratowski de no compacidad. También se entrega un ejemplo para ilustrar los resultados.

On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps

“…Hence for = 2 with the above choices, the system (3) can be rewritten to the abstract form (1) and all the conditions of Theorem 3.1 are satisfied. Thus there exists mild solutions for the system (3). Moreover all the conditions of Theorem 3.2 are satisfied and hence the fractional stochastic differential equations with Poisson jumps ( 3) is approximately controllable on '.…”

“…Many authors (see [21,22,23,30,39]) established the existence and approximate controllability of different types of functional differential equations with state-dependent delay. Fractional differential equations with state-dependent delay appear frequently in applications as models of equations and for this reason the study of this type of equations has been receiving great attention in recent years (see [3,7,43,45] and references therein). Many authors (see [13,19,26,48,51]…”

Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

“…Integro-differential equations play an important role in many branches of linear and non linear functional analysis and their applications in the theory of engineering, mechanics, physics, chemistry, biology, economics, and electrostatics. In recent years, impulsive integro-differential equations have become an important object of investigation stimulated by their numerous applications to problems in mechanics, electrical engineering, medicine, biology, ecology and so forth [14][15][16][17][18][19]. Gürbüz studied the estimation and behavior of a class of fractional type rough higher order commutators, sublinear operators, and multi-sublinear operators on generalized weighted Morrey spaces [20][21][22][23][24][25].…”

Existence results for fractional delay integro-differential equations with multi-point boundary conditions

“…Shri Akiladevi and Balachandran [16] discussed the existence and uniqueness of solution to the fractional delay integrodifferential equations with four-point multiterm fractional integral boundary conditions. The fractional differential equations with delay has drawn the attention of researchers in the recent years, for detail we refer [1], [2], [3], [9], [18], [21]. Motivated by this consideration, in this paper, we shall discuss the existence and uniqueness of solutions for the fractional delay integrodifferential equations with multi-point boundary conditions of the form by using appropriate fixed point theorems:…”