Browsing by Author "Yildiz, Burak"

Now showing 1 - 2 of 2

Citation - WoS: 88
Citation - Scopus: 94
New Aspects of Time Fractional Optimal Control Problems Within Operators With Nonsingular Kernel
(Amer inst Mathematical Sciences-aims, 2020) Jajarmi, Amin; Yildiz, Burak; Baleanu, Dumitru; Yildiz, Tugba Akman
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.
Citation - WoS: 36
Citation - Scopus: 42
New Discretization of Caputo-Fabrizio Derivative
(Springer Heidelberg, 2018) Yildiz, Burak; Baleanu, Dumitru; Akman, Tugba
We derive a numerical approximation, namely L1-2 formula, to the Caputo-Fabrizio derivative by using a quadratic interpolation. Quadratic and cubic convergence rates are achieved for L1 and L1-2 formulas using Lagrange interpolation, respectively. We compute Caputo-Fabrizio derivatives of some known functions both theoretically and numerically. In addition, we solve non/linear sub-diffusion equations to test theoretical findings. Numerical results confirm the theoretically observed convergence rates.