New interpolation spaces and strict Hölder regularity for fractional abstract Cauchy problem

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...

Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces

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