On systems of fractional differential equations with the ψ‐Caputo derivative and their applications

Abstract

Systems of fractional differential equations with a general form of fractional derivative are considered. A unique continuous solution is derived using the Banach fixed point theorem. Additionally, the dependence of the solution on the fractional order and on the initial conditions are studied. Then the stability of autonomous linear fractional differential systems with order 0<α<1 of the ψ-Caputo derivative is investigated. Finally, an application of the theoretical results to the problem of the leader-follower consensus for fractional multi-agent systems is presented. Sufficient conditions are given to ensure that the tracking errors asymptotically converge to zero. The results of the paper are illustrated by some examples.