In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.

In this paper, we establish a set of sufficient conditions for the controllability of nonlocal impulsive functional integrodifferential evolution systems with finite delay. The controllability results are obtained with out assuming the compactness condition on the evolution operator by using the semigroup theory and applying the fixed point approach. An example is provided to illustrate the the...

We have suggested the numerical schemes of collocation methods for approximative solution of singular integrodifferential equations with kernels of Cauchy type. The equations are defined on the arbitrary smooth closed contours of complex plane. The researched methods are based on Fejér points. Theoretical background of collocation methods has been obtained in Generalized Hölder spaces. Singular...

We have elaborated the numerical schemes of reduction method by FaberLaurent polynomials for the approximate solution of system of singular integrodifferential equations. The equations are defined on the arbitrary smooth closed contour. The theoretical foundation has been obtained in Lebesgue spaces. Key–Words: singular integrodifferential equations, reduction method, Lebesgue spaces

This paper deals with a class of integrodifferential impulsive periodic systems with time-varying generating operators on Banach space. Using impulsive periodic evolution operator given by us, the suitable T0-periodic PC-mild solution is introduced and Poincaré operator is constructed. Showing the compactness of Poincaré operator and using a new generalized Gronwall’s inequality with impulse, m...

We establish sufficient conditions for controllability of neutral impulsive stochastic quasilinear integrodifferential systems with nonlocal conditions in Hilbert spaces. The results are obtained by using semigroup theory, evolution operator and a fixed point technique. An example is provided to illustrate the obtained results.

In this paper, the existence and uniqueness of a fuzzy solution for the impulsive nonlinear fuzzy integrodifferential equation with nonlocal condition is established via the Banach fixed-point theorem approach and using the fuzzy number whose values are normal, convex, upper semicontinuous, and compactly supported interval.