On existence of solution for iterative integrodifferential equations

Abstract

The aim of the present paper is to establish the existence and uniqueness of solutions of iterative integrodifferential equations.

Existence and Uniqueness Results for Volterra-Fredholm Integro Differential Equations

“…Denition 2.1. [18] The Riemann-Liouville fractional integral of order α > 0 of a function f is dened as…”

“…In recent years, there has been a growing interest in the linear and nonlinear integro-dierential equations which are a combination of dierential and integral equations [4,6,7,18,20,25]. The nonlinear integrodierential equations play an important role in many branches of nonlinear functional analysis and their applications in the theory of engineering, mechanics, physics, electrostatics, biology, chemistry and economics [15] and signal processing [27].…”

“…These equations are vital in the study of infection models. Many papers have dealt with the existence, uniqueness and other properties of solutions of special forms of the iterative dierential equations and integro-dierential equations [17,18,21,22].…”

“…Kendre et al [18], studied the existence of solution for iterative integro-dierential equations of the type…”

On controllability of mixed iterative integrodifferential equations of fractional order

“…Many recent papers have handled the existence, uniqueness and other properties of solutions of unique forms of the equations (2.4) -(2.5) and (3.1) -(3.3), see ([14], [17], [19]- [23], [25,26], [29]- [31]) and some of the references quoted therein. In a thought provoking paper [15], V. Govindraj and R. George invistigated special form of (2.4) -(2.5) and (3.1) -(3.3) and provided some suitable sufficient conditions for the controllability of nonlinear iterative fractional integrodifferential systems.…”