On systems of fractional differential equations with the ψ‐Caputo derivative and their applications. (31st May 2019)

• Record Type: Journal Article
• Authors: Almeida, Ricardo; Malinowska, Agnieszka B.; Odzijewicz, Tatiana
• Other Names: Zeidan Dia guestEditor.; Herbst R Sheldon guestEditor.; Lu Tzon‐Tzer guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 10(2021)
• Page Start: 8026
• Page End: 8041
• Publication Date: 2019-05-31
• Subjects: asymptotic stability -- consensus -- fractional calculus -- fractional differential systems -- multi‐agent systems; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5678
• Languages: English
• ISSNs: 0170-4214

Abstract

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.