Existence, Uniqueness and Data Dependence for the Solutions of some Integro-Differential Equations of Mixed Type in Banach Space

Abstract

In this paper we study existence, uniqueness and data dependence for the solutions of some integro-differential equations of mixed type in Banach space by using Picard and weakly Picard operators' technique and suitable Bielecki norms.

Analysis of Volterra Integrodifferential Equations with Nonlocal and Boundary Conditions via Picard Operator

“…So there are several attractive points to investigate the solutions of the various types of differential equations. On the other hand, we can also highlight the integrodifferential equations that have gained prominence in the scientific community [5,7,8,9,10,11,12,13,14].…”

On the Nonlinear Impulsive Volterra-Fredholm Integrodifferential Equations

“…On the other hand, Anguraj et al [13], using semigroup theory and contraction mapping principle, proved the existence and uniqueness of the mild and classical solutions for the impulsive evolution mixed Volterra-Fredholm integrodifferential equation. Muresan [14] explored existence, uniqueness and data dependence of the solutions to mixed Volterra-Fredholm integrodifferential equation in Banach space by Utilizing Picard and weakly Picard operators method and Bielecki norms.…”

“…Motivated by works [4,12,13,14], we will investigate the existence, uniqueness and continuous data dependence of solutions of nonlinear Volterra-Fredholm impulsive integrodifferential equations (VFIIDEs) of the form:…”

On the approximate solution of integro-differential equations arising in oscillating magnetic fields

“…See e.g. [1], [4], [12]. For instance, using Theorem 4 in [4], we can obtain the existence and uniqueness issues for the second kind integro-differential equation (1.1).…”