Fractional abstract Cauchy problem with order $\alpha \in (1,2)$

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...

Hölder Regularity for Abstract Fractional Cauchy Problems with Order in (0,1)

In this paper, we study the regularity of mild solution for the following fractional abstract Cauchy problem ( ) ( ) ( ), (0, ] t D u t Au t f t t T α = + ∈ (0) u = 0 x on a Banach space X with order (0,1) α ∈ , where the fractional derivative is understood in the sense of Caputo fractional derivatives. We show that if A generates an analytic α-times resolvent family on X and ([0, ]; ) p f L T ...

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.