A New Formulation of the Fractional Optimal Control Problems Involving Mittag–Leffler Nonsingular Kernel

Dumitru Baleanu (), Amin Jajarmi () and Mojtaba Hajipour ()
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Dumitru Baleanu: Cankaya University
Amin Jajarmi: University of Bojnord
Mojtaba Hajipour: Sahand University of Technology

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 3, No 6, 718-737

Abstract: Abstract The aim of this paper is to propose a new formulation of the fractional optimal control problems involving Mittag–Leffler nonsingular kernel. By using the Lagrange multiplier within the calculus of variations and by applying the fractional integration by parts, the necessary optimality conditions are derived in terms of a nonlinear two-point fractional boundary value problem. Based on the convolution formula and generalized discrete Grönwall’s inequality, the numerical scheme for solving this problem is developed and its convergence is proved. Numerical simulations and comparative results show that the suggested technique is efficient and provides satisfactory results.

Keywords: Fractional calculus; Mittag–Leffler kernel; Fractional optimal control; Euler method; 26A33; 33E12; 49XX; 49K99 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-017-1186-0

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