New aspects of time fractional optimal control problems within operators with nonsingular kernel

By Tugba Akman Yildiz, Amin Jajarmi, Burak Yıldız, Dumitru Băleanu. Discrete and Continuous Dynamical Systems. Series A, 2020

88 citations recorded by the source corpus.

This paper deals with a new formulation of time fractional optimal control problems governed by Caputo-Fabrizio (CF) fractional derivative. The optimality system for this problem is derived, which contains the forward and backward fractional differential equations in the sense of CF. These equations are then expressed in terms of Volterra integrals and also solved by a new numerical scheme based on approximating the Volterra integrals. The linear rate of convergence for this method is also justified theoretically. We present three illustrative examples to show the performance of this method. These examples also test the contribution of using CF derivative for dynamical constraints and we observe the efficiency of this new approach compared to the classical version of fractional operators.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a5298fea9bd9726b251242b4f32e4b1241e9e70a

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In Applied Mathematics

1. Delfim F. M. Torres
2. Rui A. C. Ferreira
3. Agnieszka B. Malinowska
4. Gastão S. F. Frederico

In Modeling and Simulation

1. Adnane Boukhouima
2. Noura Yousfi
3. Khalid Hattaf
4. Delfim F. M. Torres
5. Elachaak Lotfi
6. Marouane Mahrouf
7. Rui A. C. Ferreira
8. Loïc Bourdin

In Numerical Analysis

1. Delfim F. M. Torres

Citations in the corpus

• Lyapunov functions for fractional-order systems in biology: Methods and applications (2020, methodology): “[64] formulate new time FOCPs governed by Caputo– Fabrizio FD.”