Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem

On the Solvability of an Inverse Fractional Abstract Cauchy Problem

This note is devoted to study an inverse Cauchy problem in a Hilbert space H for fractional abstract differential equations of the form; ), ( ) ( ) ( = ) ( t g t f t u A dt t u d    with the initial condition H u u = (0) 0 and the overdetermination condition: ), ( = ) ), ( ( t w v t u where (.,.) is the inner product in H , f is a real unknown function w is a given real function, 0 u , v ar...

Fractional Cauchy transforms

This is a survey of research on the topic of fractional Cauchy transforms. c © 1999 Elsevier Science B.V. All rights reserved.

Inhomogeneous Two-Parameter Abstract Cauchy Problem

Nonlocal Cauchy Problem for Nonautonomous Fractional Evolution Equations

During the past decades, the fractional differential equations have been proved to be valuable tools in the investigation of many phenomena in engineering and physics; they attracted many researchers cf., e.g., 1–9 . On the other hand, the autonomous and nonautonomous evolution equations and related topics were studied in, for example, 6, 7, 10–20 , and the nonlocal Cauchy problem was considere...

A Nonlocal Cauchy Problem for Fractional Integrodifferential Equations

This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach space X. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness and the fixed point theorem for condensing maps. As an application, the existence of the mild solution to a nonlocal Cauchy problem for a conc...