We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter whose coefficients depend holomorphically on ( , t) near the origin in C and are bounded holomorphic on some horizontal strip in C w.r.t the space variable. In our previous contribution [14], we assumed the forcing term of the Cauchy problem to be analytic near 0. Presently, we consider a family of...

Abstract We know that interpolation spaces in terms of analytic semigroup have a significant role into the study strict Hölder regularity solutions classical abstract Cauchy problem (ACP). In this paper, we first construct solution operators fractional calculus and characterize these spaces. Then establish mild order ACP.

In this paper, as an improvement of the paper (Ishige et al. in SIAM J Math Anal 49:2167–2190, 2017), we obtain higher order asymptotic expansions large time behavior solution to Cauchy problem for inhomogeneous fractional diffusion equations and nonlinear equations.

The questions of the existence and uniqueness solution to Cauchy problem for an equation in a Banach space distributed order at most one are investigated. Necessary sufficient conditions resolving family operators this analytic sector obtained. An explicit form these is found. Two versions theorem on unique solvability corresponding inhomogeneous obtained: with condition increased smoothness sp...