Existence of solutions for nonlocal impulsive partial functional integrodifferential equations via fractional operators

AbstractIn this paper, by using the Leray–Schauder alternative, we have investigated the existence of mild solutions to first-order impulsive partial functional integrodifferential equations with nonlocal conditions in an α-norm. We assume that the linear part generates an analytic compact bounded semigroup, and that the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part. An example is also given to illustrate our main results

Nonlinear functional integrodifferential evolution equations with nonlocal conditions in Banach spaces

In this paper, the Leray-Schauder Alternative is used to investigate the existence of mild solutions to first-order nonlinear functional integrodifferential evolution equations with nonlocal conditions in Banach spaces

ON A NONLINEAR INTEGRODIFFERENTIAL EVOLUTION INCLUSION WITH NONLOCAL INITIAL CONDITIONS IN BANACH SPACES

Abstract. In this paper, we discuss the existence results for a class of nonlinear integrodifferential evolution inclusions with nonlocal initial conditions in Banach spaces. Our results are based on a fixed point theorem for condensing maps due to Martelli and the resolvent operators combined with approximation techniques

On Approximate Controllability of Second-Order Neutral Partial Stochastic Functional Integrodifferential Inclusions with Infinite Delay and Impulsive Effects

We discuss the approximate controllability of second-order impulsive neutral partial stochastic functional integrodifferential inclusions with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using the fixed point strategy, stochastic analysis, and properties of the cosine family of bounded linear operators combined with approximation techniques, a new set of sufficient conditions for approximate controllability of the second-order impulsive partial stochastic integrodifferential systems are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result

On a nonlinear integrodifferential evolution inclusion with nonlocal initial conditions in Banach spaces

Tyt. z nagłówka.Bibliogr. s. 392-394.In this paper, we discuss the existence results for a class of nonlinear integrodifferential evolution inclusions with nonlocal initial conditions in Banach spaces. Our results are based on a fixed point theorem for condensing maps due to Martelli and the resolvent operators combined with approximation techniques.Dostępny również w formie drukowanej.KEYWORDS: nonlinear integrodifferential evolution inclusions, fixed point, resolvent operator, nonlocal initial condition

Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay

In this article, we study the asymptotical stability in p-th moment of mild solutions to a class of fractional impulsive partial neutral stochastic integro-differential equations with state-dependent delay in Hilbert spaces. We assume that the linear part of this equation generates an alpha-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence and asymptotic stability of solutions are derived by means of the Krasnoselskii-Schaefer type fixed point theorem and properties of the alpha-resolvent operator. An illustrative example is also provided