A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation

Fardi, Mojtaba; Al‐Omari, Shrideh; Aracı, Serkan

doi:10.1186/s13662-022-03726-4

Cited by 12 publications

(3 citation statements)

References 45 publications

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“…The surge in attention towards fractional partial differential equations (FPDEs) over recent decades reflects a growing recognition of their versatile applicability across various domains of physics and engineering [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Among the rich tapestry of FPDEs, one stands out prominently: the time fractional diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

Efficient Numerical Solutions for Fuzzy Time Fractional Diffusion Equations Using Two Explicit Compact Finite Difference Methods

Batiha

2024

Computation

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This article introduces an extension of classical fuzzy partial differential equations, known as fuzzy fractional partial differential equations. These equations provide a better explanation for certain phenomena. We focus on solving the fuzzy time diffusion equation with a fractional order of 0 < α ≤ 1, using two explicit compact finite difference schemes that are the compact forward time center space (CFTCS) and compact Saulyev’s scheme. The time fractional derivative uses the Caputo definition. The double-parametric form approach is used to transfer the governing equation from an uncertain to a crisp form. To ensure stability, we apply the von Neumann method to show that CFTCS is conditionally stable, while compact Saulyev’s is unconditionally stable. A numerical example is provided to demonstrate the practicality of our proposed schemes.

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Section: Introductionmentioning

confidence: 99%

Efficient Numerical Solutions for Fuzzy Time Fractional Diffusion Equations Using Two Explicit Compact Finite Difference Methods

Batiha

2024

Computation

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“…Huang et al [29] developed efficient schemes for solving a non-linear TFDWE involving CFD. A pseudo-spectral scheme that depends on a reproducing kernel has been proposed by Fardi et al [30]. Chen et al [31] presented numerical and analytical solutions for a TFDWE with damping.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of the Fractional Diffusion Wave Equation with the Mittag–Leffler Function

Shafiq,

Abbas,

El-Shewy

et al. 2023

Fractal Fract

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A spline is a sufficiently smooth piecewise curve. B-spline functions are powerful tools for obtaining computational outcomes. They have also been utilized in computer graphics and computer-aided design due to their flexibility, smoothness and accuracy. In this paper, a numerical procedure dependent on the cubic B-spline (CuBS) for the time fractional diffusion wave equation (TFDWE) is proposed. The standard finite difference (FD) approach is utilized to discretize the Atangana–Baleanu fractional derivative (ABFD), while the derivatives in space are approximated through the CuBS with a θ-weighted technique. The stability of the propounded algorithm is analyzed and proved to be unconditionally stable. The convergence analysis is also studied, and it is of the order O(h2+(Δt)2). Numerical solutions attained by the CuBS scheme support the theoretical solutions. The B-spline technique gives us better results as compared to other numerical techniques.

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“…The q-analogue of the Ruscheweyh operator was also studied in [26][27][28]. For more details on this theory, we refer to [29][30][31][32][33][34][35][36][37][38][39][40][41][42] and references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Results on Univalent Functions Defined by q-Analogues of Salagean and Ruscheweh Operators

et al. 2022

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In this paper, we define and discuss properties of various classes of analytic univalent functions by using modified q-Sigmoid functions. We make use of an idea of Salagean to introduce the q-analogue of the Salagean differential operator. In addition, we derive families of analytic univalent functions associated with new q-Salagean and q-Ruscheweh differential operators. In addition, we obtain coefficient bounds for the functions in such new subclasses of analytic functions and establish certain growth and distortion theorems. By using the concept of the (q, δ)-neighbourhood, we provide several inclusion symmetric relations for certain (q, δ)-neighbourhoods of analytic univalent functions of negative coefficients. Various q-inequalities are also discussed in more details.

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A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation

Cited by 12 publications

References 45 publications

Efficient Numerical Solutions for Fuzzy Time Fractional Diffusion Equations Using Two Explicit Compact Finite Difference Methods

Efficient Numerical Solutions for Fuzzy Time Fractional Diffusion Equations Using Two Explicit Compact Finite Difference Methods

Numerical Investigation of the Fractional Diffusion Wave Equation with the Mittag–Leffler Function

Results on Univalent Functions Defined by q-Analogues of Salagean and Ruscheweh Operators

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