An Initial Problem for a Class of Weakly Degenerate Semilinear Equations with Lower Order Fractional Derivatives

Abstract

An initial value problem is studied for a class of evolutionary equations with a weak degeneration, which are nonlinear with respect to lower order fractional Gerasimov – Caputo derivatives. The linear part of the equations contains a respectively bounded pair of operators. Unique local solvability is proved in the case of a nonlinear operator depending on elements of the degeneration space only. Examples of an equation and a system of partial differential equations are given, the initial-boundary value problems for which are reduced to the initial problem for an equation in a Banach space of the studied class.

Keywords

• fractional gerasimov – caputo derivative
• fractional order differential equation
• degenerate evolution equation
• semilinear equation