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In this article, we study the concept of Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations. We establish the results with Lipschitz condition and without Lipschitz condition on the forcing term. An interesting example is presented to illustrate the main findings. The results proven are new and complement the existing ones.Keywords. Fractional order abstract integro-differential equations; Stepanov-like weighted pseudo almost automorphy.

This paper is concerned with the existence of mild solutions for partial neutral functional integrodifferential equations with infinite delay in a Banach space. The results are obtained by using the resolvent operators and Krasnoselski-Schaefer type fixed point theorem. An example is given to illustrate the results.

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

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In this paper, we study the existence of integral solutions for impulsive evolution equations with nonlocal conditions where the linear part is nondensely defined. Some existence results of integral solutions to such problems are obtained under the conditions in respect of the Hausdorff's measure of noncompactness. Example is provided to illustrate the main result.