&lt;i&gt;ψ&lt;/i&gt;-SHIFTED OPERATIONAL MATRIX SCHEME FOR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Sadiq, Shazia; Rehman, Mujeeb ur

doi:10.11948/20210101

Cited by 2 publications

(2 citation statements)

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“…Here we discuss a few most important definitions and properties related to ψ fractional integrals and derivatives (Almeida et al, 2019;Almeida, 2017;Sadiq and Rehman, 2022b…”

Section: Preliminariesmentioning

confidence: 99%

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A generalized CAS wavelet method for solving ψ-Caputo fractional differential equations

Saeed

2023

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PurposeThe purpose of the present work is to introduce a wavelet method for the solution of linear and nonlinear psi-Caputo fractional initial and boundary value problem.Design/methodology/approachThe authors have introduced the new generalized operational matrices for the psi-CAS (Cosine and Sine) wavelets, and these matrices are successfully utilized for the solution of linear and nonlinear psi-Caputo fractional initial and boundary value problem. For the nonlinear problems, the authors merge the present method with the quasilinearization technique.FindingsThe authors have drived the orthogonality condition for the psi-CAS wavelets. The authors have derived and constructed the psi-CAS wavelets matrix, psi-CAS wavelets operational matrix of psi-fractional order integral and psi-CAS wavelets operational matrix of psi-fractional order integration for psi-fractional boundary value problem. These matrices are successfully utilized for the solutions of psi-Caputo fractional differential equations. The purpose of these operational matrices is to make the calculations faster. Furthermore, the authors have derived the convergence analysis of the method. The procedure of implementation for the proposed method is also given. For the accuracy and applicability of the method, the authors implemented the method on some linear and nonlinear psi-Caputo fractional initial and boundary value problems and compare the obtained results with exact solutions.Originality/valueSince psi-Caputo fractional differential equation is a new and emerging field, many engineers can utilize the present technique for the numerical simulations of their linear/non-linear psi-Caputo fractional differential models. To the best of the authors’ knowledge, the present work has never been introduced and implemented for psi-Caputo fractional differential equations.

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“…Here we discuss a few most important definitions and properties related to ψ fractional integrals and derivatives (Almeida et al, 2019;Almeida, 2017;Sadiq and Rehman, 2022b…”

Section: Preliminariesmentioning

confidence: 99%

“…The method is based on ψ -shifted Chebyshev polynomials. These polynomials are also utilized in Sadiq and Rehman (2022b) for solving time-space ψ -fractional partial differential equations. Authors (Norouzi and N’Guérékata, 2021) studied the existence and uniqueness of the system of ψ -Hilfer fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

A generalized CAS wavelet method for solving ψ-Caputo fractional differential equations

Saeed

2023

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Numerical Methods for the Caputo-Type Fractional Derivative With an Exponential Kernel

Fan¹,

Li²,

Li³

2023

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<i>ψ</i>-SHIFTED OPERATIONAL MATRIX SCHEME FOR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Cited by 2 publications

References 30 publications

A generalized CAS wavelet method for solving ψ-Caputo fractional differential equations

A generalized CAS wavelet method for solving ψ-Caputo fractional differential equations

Numerical Methods for the Caputo-Type Fractional Derivative With an Exponential Kernel

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