Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives

Mathematics

Vladimir E. Fedorov¹  Wei-Shih Du²  Aliya A. Abdrakhmanova³  Marko Kostić⁴ 

[1] Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers Str. 129, 454001 Chelyabinsk, Russia;Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan;Department of Mathematics, Ufa State Aviation Technical University, Karl Marks Str. 12, 450077 Ufa, Russia;Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia;

关键词: Riemann–Liouville derivative;    distributed order equation;    analytic resolving family of operators;    generator of resolving family;    perturbation theorem;   

DOI  :  10.3390/math10050681

来源: DOAJ

【 摘 要 】

Some new necessary and sufficient conditions for the existence of analytic resolving families of operators to the linear equation with a distributed Riemann–Liouville derivative in a Banach space are established. We study the unique solvability of a natural initial value problem with distributed fractional derivatives in the initial conditions to corresponding inhomogeneous equations. These abstract results are applied to a class of initial boundary value problems for equations with distributed derivatives in time and polynomials with respect to a self-adjoint elliptic differential operator in spatial variables.

【 授权许可】

Unknown