According to semigroup theories and Sadovskii fixed point theorem, this paper is mainly concerned with the existence of solutions for an impulsive neutral differential and integrodifferential systems with nonlocal conditions in Banach spaces. As an application of this main theorem, a practical consequence is derived for the sub-linear growth case. In the end, an example is also given to show th...

By applying hybrid functions of general block-pulse functions and the second Chebyshev polynomials, integrodifferential systems are converted into a system of algebraic equations. The approximate solutions of integrodifferential systems are derived. The numerical examples illustrate that the algorithms are valid.

We study the solvability of the fractional integrodifferential equations of neutral type with infinite delay in a Banach space X. An existence result of mild solutions to such problems is obtained under the conditions in respect of Kuratowski's measure of noncompactness. As an application of the abstract result, we show the existence of solutions for an integrodifferential equation.

In this paper, we establish a sufficient condition for the controlla-bility of impulsive quasi-linear fractional mixed Volterra-Fredholm-type inte-grodifferential equations in Banach spaces. The results are obtained by using Banach contraction fixed point theorem combined with the fractional calculus theory.

In this paper, we study the existence and uniqueness of nonlinear fuzzy neutral integrodifferential equations. We also establish the controllability of nonlinear fuzzy neutral integrodifferential systems. The results are obtained in this paper are mainly based on the fuzzy strongly continuous semigroup theory. An example is provided to illustrate the main results of this paper.

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

Correspondence: fangli860@gmail. com School of Mathematics, Yunnan Normal University, Kunming 650092, People’s Republic of China Abstract This article concerns the existence of mild solutions for the fractional integrodifferential equations of neutral type with finite delay and nonlocal conditions in a Banach space X. The existence of mild solutions is proved by means of measure of noncompactne...

The question is studied whether weak solutions of linear partial integrodifferential equations approach a constant spatial profile after rescaling, as time goes to infinity. The possible limits and corresponding scaling functions are identified and are shown to actually occur. The limiting equations are fractional diffusion equations which are known to have self-similar fundamental solutions. F...