Vladimir E. Fedorov, Elizaveta M. Streletskaya
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.
Submitted August 13, 2018. Published October 30, 2018.
Math Subject Classifications: 35R11, 34G10, 47D99, 34A08.
Key Words: Distributed order differential equation;
fractional Caputo derivative; differential equation in a Banach space;
degenerate evolution equation; Cauchy problem.
Show me the PDF file (302 KB), TEX file for this article.
 |
Vladimir E. Fedorov Mathematical Analysis Department Chelyabinsk State University 129 Kashirin Brothers St. Chelyabinsk, 454001 Russia email: kar@csu.ru |
|---|---|
 |
Elizaveta M. Streletskaya Mathematical Analysis Department Chelyabinsk State University 129 Kashirin Brothers St. Chelyabinsk, 454001 Russia email: wwugazi@gmail.com |
Return to the EJDE web page