Initial-value problems for linear distributed-order differential equations in Banach spaces
Date
2018-10-30
Authors
Fedorov, Vladimir
Streletskaya, Elizaveta
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We solve the Cauchy problem for inhomogeneous distributed-order equations in a Banach space with a linear bounded operator in the right-hand side, with respect to the distributed Caputo derivative. First we find the solution by using the unique solvability theorem for the Cauchy problem. Then the results obtained are applied to the analysis of a distributed-order system of ordinary differential equations. Then we study an analogous equation, but with degenerate linear operator at the distributed derivative, which is called a degenerate equation. The pair of linear operators in the equation is assumed to be relatively bounded. For the two types of initial-value problems, we obtain the existence and uniqueness of a solution, and derive its form. Abstract results for the degenerate equations are used in the study of initial-boundary value problems with distributed order in time equations with polynomials of self-adjoint elliptic differential operator with respect to the spatial derivative.
Description
Keywords
Distributed order differential equation, Fractional Caputo derivative, Differential equation in a Banach space, Degenerate evolution equation, Cauchy problem
Citation
Fedorov, V. E., & Streletskaya, E. M. (2018). Initial-value problems for linear distributed-order differential equations in Banach spaces. <i>Electronic Journal of Differential Equations, 2018</i>(176), pp. 1-17.
Rights
Attribution 4.0 International