Abstract
In this paper, a criterion for generating an analytic family of operators, which resolves a linear equation solved with respect to the Dzhrbashyan–Nersesyan fractional derivative, via a linear closed operator is obtained. The properties of the resolving families are investigated and applied to prove the existence of a unique solution for the corresponding initial value problem of the inhomogeneous equation with the Dzhrbashyan–Nersesyan fractional derivative. A solution is presented explicitly using resolving families of operators. A theorem on perturbations of operators from the found class of generators of resolving families is proved. The obtained results are used for a study of an initial-boundary value problem to a model of the viscoelastic Oldroyd fluid dynamics. Thus, the Dzhrbashyan–Nersesyan initial value problem is investigated in the essentially infinite-dimensional case. The use of the proved abstract results to study initial-boundary value problems for a system of partial differential equations is demonstrated.
Funder
Russian Science Foundation
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Reference39 articles.
1. Fractional derivatives and cauchy problem for differential equations of fractional order
2. Fractional Integrals and Derivatives. Theory and Applications;Samko,1993
3. Fractional Differential Equations;Podlubny,1999
4. Fractional Calculus ant Its Applications;Nakhushev,2003
5. Theory and Applications of Fractional Differential Equations;Kilbas,2006
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献