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Alipour, Maryam, Soradi-Zeid, Samaneh. (1405). Numerical Assessment of Optimal Control Problems with Variable Order Fractional Integro-Differential Equation Based on Laguerre Wavelets Functions. نشریه علمی دانشگاه سیستان و بلوچستان, 9(2), 199-209. doi: 10.22111/ieco.2025.52258.1695
Maryam Alipour; Samaneh Soradi-Zeid. "Numerical Assessment of Optimal Control Problems with Variable Order Fractional Integro-Differential Equation Based on Laguerre Wavelets Functions". نشریه علمی دانشگاه سیستان و بلوچستان, 9, 2, 1405, 199-209. doi: 10.22111/ieco.2025.52258.1695
Alipour, Maryam, Soradi-Zeid, Samaneh. (1405). 'Numerical Assessment of Optimal Control Problems with Variable Order Fractional Integro-Differential Equation Based on Laguerre Wavelets Functions', نشریه علمی دانشگاه سیستان و بلوچستان, 9(2), pp. 199-209. doi: 10.22111/ieco.2025.52258.1695
Alipour, Maryam, Soradi-Zeid, Samaneh. Numerical Assessment of Optimal Control Problems with Variable Order Fractional Integro-Differential Equation Based on Laguerre Wavelets Functions. نشریه علمی دانشگاه سیستان و بلوچستان, 1405; 9(2): 199-209. doi: 10.22111/ieco.2025.52258.1695

Numerical Assessment of Optimal Control Problems with Variable Order Fractional Integro-Differential Equation Based on Laguerre Wavelets Functions

International Journal of Industrial Electronics Control and Optimization
مقاله 7، دوره 9، شماره 2، شهریور 2026، صفحه 199-209    اصل مقاله (970.79 K)
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22111/ieco.2025.52258.1695
نویسندگان
Maryam Alipour1؛ Samaneh Soradi-Zeid* 2
1Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
2Faculty of Industry and Mining (khash), University of Sistan and Baluchestan, Zahedan, Iran.
چکیده
‎This paper deals with a general form of fractional optimal control problems involving variable-order fractional integro differential equation using orthonormal Laguerre wavelets expansions. By effectively employing these ‎functions,‎ product variable-order operational matrices have been obtained. By using these fractional operational matrices and collocation points, the study transforms the original continuous-time optimal control problems of variable-order fractional integro-differential equations into a system of linear or non-linear algebraic equations. ‎Attempts have been made to use the collocation method with a joint application of Lagrange multiplier technique, to obtain the approximate cost function based on determining the state and control functions. ‎The ‎main ‎components ‎for ‎applying ‎these ‎wavelets ‎is ‎to ‎have ‎viable ‎solutions ‎due ‎to ‎their ‎orthogonality.‎ ‎In addition‎, ‎the convergence analysis is presented with respect to the operational matrices of this scheme‎. Simulation results indicate that the proposed method works well and provides satisfactory results with regard to accuracy and computational effort.
کلیدواژه‌ها
Integro-differential equation؛ Variable-order fractional calculus؛ Optimal control problem؛ Laguerre wavelet؛ Collocation method
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