On systems of fractional differential equations with the ψ-Caputo derivative and their applications
Ricardo Almeida
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Search for more papers by this authorAgnieszka B. Malinowska
Faculty of Computer Science, Bialystok University of Technology, 15-351 Białystok, Poland
Search for more papers by this authorCorresponding Author
Tatiana Odzijewicz
Department of Mathematics and Mathematical Economics, Warsaw School of Economics, 02-554 Warsaw, Poland
Correspondence
Tatiana Odzijewicz, Department of Mathematics and Mathematical Economics, Warsaw School of Economics, Al. Niepodległości 162, 02-554 Warsaw, Poland.
Email: [email protected]
Communicated by: D. Zeidan
Search for more papers by this authorRicardo Almeida
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Search for more papers by this authorAgnieszka B. Malinowska
Faculty of Computer Science, Bialystok University of Technology, 15-351 Białystok, Poland
Search for more papers by this authorCorresponding Author
Tatiana Odzijewicz
Department of Mathematics and Mathematical Economics, Warsaw School of Economics, 02-554 Warsaw, Poland
Correspondence
Tatiana Odzijewicz, Department of Mathematics and Mathematical Economics, Warsaw School of Economics, Al. Niepodległości 162, 02-554 Warsaw, Poland.
Email: [email protected]
Communicated by: D. Zeidan
Search for more papers by this authorAbstract
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.
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