Temporal discretization for Caputo–Hadamard fractional derivative with incomplete Gamma function via Whittaker function

Toh, Yoke Teng; Phang, Chang; Ng, Yong Xian

doi:10.1007/s40314-021-01673-6

Cited by 9 publications

(5 citation statements)

References 34 publications

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“…The Caputo fractional derivatives are used in this context to define the time fractional derivative. FPDE can be solved using a variety of numerical techniques, including the finite element method [1], VIM [2,3], finite difference method [4,5], homotopy perturbation method [6], Tau method [7,8], operational method [9], Ritz approximation approach [10], and Caputo-Hadamard fractional derivative [11]. Recently, several numerical schemes have been created to solve the TFCDE such as Sinc-Legendre collocation method [12], discontinuous Galerkin method [13], Gegenbauer method [14], Sinc and B-spline scaling functions [15], Haar wavelet method [16], Chebyshev collocation method [17], and radial basis functions [18].…”

Section: 𝜕 𝛼 𝜇(𝜘 T)mentioning

confidence: 99%

Fibonacci wavelet method for time fractional convection–diffusion equations

Yadav,

Jahan,

Nisar

2023

Math Methods in App Sciences

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This study concentrates on time fractional convection–diffusion equations (TFCDEs) with variable coefficients and their numerical solutions. Caputo derivative is used to calculate the time fractional order derivatives. In order to give an approximate solution to the TFCDE, an effective approach is proposed utilizing Fibonacci wavelet and block pulse functions. The Fibonacci wavelets operational matrices of fractional order integration are constructed. By combining the collocation technique, they are used to simplify the fractional model to a collection of algebraic equations. The suggested approach is quite practical for resolving issues of this nature. The comparison and analysis with other approaches demonstrate the effectiveness and precision of the suggested approach.

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Section: 𝜕 𝛼 𝜇(𝜘 T)mentioning

confidence: 99%

Fibonacci wavelet method for time fractional convection–diffusion equations

Yadav,

Jahan,

Nisar

2023

Math Methods in App Sciences

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“…Nowadays, differential equations of fractional order as extension of the differential equations of integer order play a fundamental role in the modeling of many scientific, practical, and important problems [1][2][3][4][5][6][7][8][9][10]. Recently, several numerical methods have been proposed to simulate various types of fractional-order systems [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

An efficient numerical method for the time-fractional distributed order nonlinear Klein–Gordon equation with shifted fractional Gegenbauer multi-wavelets method

et al. 2023

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In this paper, we propose an effective numerical method, based on the use of two-dimensional Shifted fractional-order Gegenbauer Multi-wavelets, for finding the approximate solutions of the time-fractional distributed order non-linear partial differential equations. The method is applied to solve fractional distributed order non-linear Klein-Gordon equation, numerically. We derive an exact formula for the Riemann–Liouville fractionalintegral operator for the Shifted fractional Gegenbauer Multi-wavelets.Applying function approximations obtained by this method turns the considered equation into a system of algebraic equations. Error estimation and convergence analysis of the methodare also studied. Some numerical examples are included to show and check the effectiveness of the proposed method.

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“…The works in [3,4] provide useful summaries and applications of how and where the CHFD arises. FDE within CHFD are a very important class of equations, and their applications can be found in a variety of engineering and scientific disciplines, such as mechanics, biology, chemistry, physics, the stability and instability of geodesics on Riemannian varieties, Hamiltonian systems, and technical engineering sciences [5,6].…”

Section: Introductionmentioning

confidence: 99%

On Stability of Second Order Pantograph Fractional Differential Equations in Weighted Banach Space

Dida,

Boulares,

Moumen

et al. 2023

Fractal Fract

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This work investigates a weighted Banach space second order pantograph fractional differential equation. The considered equation is of second order, expressed in terms of the Caputo–Hadamard fractional operator, and constructed in a general manner to accommodate many specific situations. The asymptotic stability of the main equation’s trivial solution has been given. The primary theorem was demonstrated in a unique manner by employing the Krasnoselskii’s fixed point theorem. We provide a concrete example that supports the theoretical findings.

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Temporal discretization for Caputo–Hadamard fractional derivative with incomplete Gamma function via Whittaker function

Cited by 9 publications

References 34 publications

Fibonacci wavelet method for time fractional convection–diffusion equations

Fibonacci wavelet method for time fractional convection–diffusion equations

An efficient numerical method for the time-fractional distributed order nonlinear Klein–Gordon equation with shifted fractional Gegenbauer multi-wavelets method

On Stability of Second Order Pantograph Fractional Differential Equations in Weighted Banach Space

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