Riemann–Liouville abstract fractional Cauchy problem with damping

Inhomogeneous Two-Parameter 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...

inhomogeneous two-parameter abstract cauchy problem

A singular abstract cauchy problem.

In this note a singular abstract Cauchy problem is considered. A solution is obtained for this problem in terms of a regular abstract Cauchy problem. As an application we obtain a new solution of the initial value problem for a class of singular partial differential equations.

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...