The Well-Posedness of Incommensurate FDEs in the Space of Continuous Functions

Abstract

A system of fractional differential equations (FDEs) with fractional derivatives of diverse orders is called an incommensurate system of FDEs. In this paper, the well-posedness of the initial value problem for incommensurate systems of FDEs is obtained on the space of continuous functions. Three different methods for this analysis are used and compared. The complexity of such analysis is reduced by new techniques. Strong existence results are obtained by weaker conditions. The uniqueness and the continuous dependency of the solution on initial values are investigated using the Gronwall inequality.

Keywords

• fractional differential equations
• Gronwall inequality
• well-posed problem
• existence result
• Schauder fixed-point theorem