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 investigate infinite interval problems for the fractional evolution equations with Hilfer derivative. By using generalized Ascoli–Arzelà theorem and some new techniques, prove existence of mild solutions when semigroup is compact as well noncompact. addition, an example provided to illustrate results.

This paper addresses some existence, attractivity and controllability results for semilinear integrodifferential equations having non-instantaneous impulsions on an infinite interval via resolvent operators in case of neutral state-dependent delay problems. Our criteria were obtained by applying a Darbo’s fixed-point theorem combined with measures noncompactness. The result is illustrated examp...

In this paper, we study the existence of extremal solutions for impulsive delay fuzzy integrodifferential equations in n-dimensional fuzzy vector space, by using monotone method. We show that obtained result is an extension of the result of Rodŕıguez-López [8] to impulsive delay fuzzy integrodifferential equations in n-dimensional fuzzy vector space.

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

Many dynamic systems can be modeled by fractional differential equations in which some external parameters occur under uncertainty. Although these increase the complexity, they present more acceptable solutions. With aid of Atangana-Baleanu-Caputo (ABC) operator, an advanced numerical-analysis approach is considered and applied this work to deal with different classes fuzzy integrodifferential ...

in this paper, we study the existence of extremal solutions forimpulsive delay fuzzy integrodifferential equations in$n$-dimensional fuzzy vector space, by using monotone method. weshow that obtained result is an extension of the result ofrodr'{i}guez-l'{o}pez cite{rod2} to impulsive delay fuzzyintegrodifferential equations in $n$-dimensional fuzzy vector space.

The objective of this paper is to investigate the existence mild solutions and optimal controls for a class fractional neutral stochastic integrodifferential equations driven by Rosenblatt process Poisson jumps in Hilbert spaces. First we establish new set sufficient conditions aforementioned systems using successive approximation approach. results are formulated proved calculus, solution opera...