Fractional-order Boubaker wavelets method for solving fractional Riccati differential equations

Rabiei, Kobra; Razzaghi, Mohsen

doi:10.1016/j.apnum.2021.05.017

Cited by 18 publications

(10 citation statements)

References 34 publications

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“…Similarly to [46], it is noted that the convergence of the our method can be reduced to the convergence of the function approximation occurring in Equations () and () and the integration occurring in Equation (), which are given in Theorem 5.1 and 5.2, respectively.…”

Section: Error Analysismentioning

confidence: 99%

An approximate solution for variable‐order fractional optimal control problem via Müntz‐Legendre wavelets with an application in epidemiology

Razzaghi

Iordache

2023

Math Methods in App Sciences

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A class of variable‐order fractional optimal control problems (VO‐FOCPs) is solved by applying Müntz‐Legendre wavelets. Different from classical wavelets (such as Legendre and Chebyshev), the Müntz‐Legendre wavelets have an extra parameter representing the fractional order; therefore, they provide more reliable results for certain fractional calculus problems. Using the regularized beta function, the Riemann‐Liouville fractional integral operator (RLFIO) of these wavelets is precisely determined. We then transform the given VO‐FOCPs into parameter optimization problems that can be easily solved. The convergence analysis and error estimation of the proposed method are provided. Four examples are solved to illustrate the high accuracy of the approach. The method is also applied to a cancer‐obesity interaction model to analyze the interactions between the tumor, immune, normal, and fat cells when the chemotherapeutic drugs are injected into a body.

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Section: Error Analysismentioning

confidence: 99%

An approximate solution for variable‐order fractional optimal control problem via Müntz‐Legendre wavelets with an application in epidemiology

Razzaghi

Iordache

2023

Math Methods in App Sciences

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“…Due to the tremendous difficulty of finding exact solutions for many types of FDEs, many researchers have been interested in obtaining analytical and numerical solutions for such problems. Some of them are the finite difference (Hendy et al (2021)), predictor-corrector (Kumar and Gejji (2019)), wavelet operational matrix (Yi and Huang ( 2014)), Galerkin-Legendre spectral (Zaky et al (2020)), fractional-order Boubaker wavelets (Rabiei and Razzaghi (2021)), fractional Jacobi collocation (Abdelkawy et al (2020)) and artificial neural network (Pakdaman et al 2017) methods. Because of the globality of fractional calculus, it is preferable to use global numerical techniques to solve FDEs of various types.…”

Section: Introductionmentioning

confidence: 99%

Robust spectral treatment for time-fractional delay partial differential equations

2023

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Fractional delay differential equations (FDDEs) and time-fractional delay partial differential equations (TFDPDEs) are the focus of the present research. The FDDEs is converted into a system of algebraic equations utilizing a novel numerical approach based on the spectral Galerkin (SG) technique. The suggested numerical technique is likewise utilized for TFDPDEs. In terms of shifted Jacobi polynomials, suitable trial functions are developed to fulfill the initial-boundary conditions of the main problems. According to the authors, this is the first time utilizing the SG technique to solve TFDPDEs. The approximate solution of five numerical examples is provided and compared with those of other approaches and with the analytic solutions to test the superiority of the proposed method.

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“…Many researchers worked on several wavelets for the solutions of fractional differential equations. Some of these wavelets include Haar wavelets (Saeed and Rehman, 2013), Chebyshev wavelets (Saeed and Saeed, 2019; Heydari et al ., 2022), Gegenbauer wavelets (Saeed et al ., 2021; Rehman and Saeed, 2015), Sine–Cosine wavelets (Idrees and Saeed, 2022), CAS wavelets (Yousefi and banifatemi, 2006; Saeed, 2017), Boubaker wavelets (Rabiei and Razzaghi, 2021), Taylor wavelets (Toan et al ., 2021), Chebyshev cardinal wavelets (Heydari and Razzaghi, 2023), Chelyshkov wavelet (Ngo et al ., 2023), etc.…”

Section: Introductionmentioning

confidence: 99%

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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Fractional-order Boubaker wavelets method for solving fractional Riccati differential equations

Cited by 18 publications

References 34 publications

An approximate solution for variable‐order fractional optimal control problem via Müntz‐Legendre wavelets with an application in epidemiology

An approximate solution for variable‐order fractional optimal control problem via Müntz‐Legendre wavelets with an application in epidemiology

Robust spectral treatment for time-fractional delay partial differential equations

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

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