Implementation of an Optimization Algorithm for a New General Class of Two-Dimensional Fractional PDEs

Zakieh Avazzadeh (), Hossein Hassani (), Mohammad Javad Ebadi (), Ali Bayati Eshkaftaki () and Ahmed Hendy ()
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Zakieh Avazzadeh: Stony Brook Institute at Anhui University, Anhui University
Hossein Hassani: Anand International College of Engineering
Mohammad Javad Ebadi: Chabahar Maritime University
Ali Bayati Eshkaftaki: Shahrekord University
Ahmed Hendy: Benha University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 4, 22 pages

Abstract: Abstract In recent years, the inherent numerical difficulties in the study of two-dimensional fractional differential equations (T-FDEs) make them challenging for investigation. In the present contribution, we introduce a new general class of T-FDEs to be solved. Their solution is addressed by the use of unique polynomials of the generalized shifted Legendre functions. For this purpose, we evaluate the association of new fractional and ordinary operational matrices using the Lagrange multipliers algorithm. The analysis of the convergence is done and the existence of a unique solution for the T-FDEs is proved. Three problems are considered to test the proposed methodology. It is pointed out that our methodology can be considered as a promising strategy to solve two-dimensional variable-order fractional differential equations and 2D variable-order fractional optimal control problems.

Keywords: General class of two-dimensional fractional differential equations; Generalized shifted Legendre polynomials; Optimization method; Fractional operational matrices; Lagrange multipliers (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02643-2

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