A New Scheme for Solving Multiorder Fractional Differential Equations Based on Müntz–Legendre Wavelets | Zendy

Haifa Bin Jebreen | Zendy; Fairouz Tchier | Zendy

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A New Scheme for Solving Multiorder Fractional Differential Equations Based on Müntz–Legendre Wavelets

Author(s) -

Haifa Bin Jebreen,

Fairouz Tchier

Publication year - 2021

Publication title -

complexity

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.447

H-Index - 61

eISSN - 1099-0526

pISSN - 1076-2787

DOI - 10.1155/2021/9915551

Subject(s) - legendre wavelet , legendre polynomials , mathematics , algebraic equation , chebyshev filter , wavelet , fractional calculus , operator (biology) , matrix (chemical analysis) , chebyshev pseudospectral method , scheme (mathematics) , derivative (finance) , algebraic number , mathematical analysis , chebyshev equation , computer science , wavelet transform , nonlinear system , discrete wavelet transform , classical orthogonal polynomials , materials science , repressor , artificial intelligence , chemistry , financial economics , composite material , biochemistry , quantum mechanics , transcription factor , physics , economics , gene , orthogonal polynomials

In this study, we apply the pseudospectral method based on Müntz–Legendre wavelets to solve the multiorder fractional differential equations with Caputo fractional derivative. Using the operational matrix for the Caputo derivative operator and applying the Chebyshev and Legendre zeros, the problem is reduced to a system of linear algebraic equations. We illustrate the reliability, efficiency, and accuracy of the method by some numerical examples. We also compare the proposed method with others and show that the proposed method gives better results.

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