Utilization of Haar wavelet collocation technique for fractal-fractional order problem

Shah, Kamal; Amin, Rohul; Abdeljawad, Thabet

doi:10.1016/j.heliyon.2023.e17123

Cited by 7 publications

(2 citation statements)

References 18 publications

(19 reference statements)

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“…Fractional calculus (FC) is the generalization of classical calculus, which includes integrals and derivatives in non-integer order [1,2]. In recent years, the concept of fractional derivatives has been applied with great success to model various real-life phenomena in many scientific fields [3].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Advection–Diffusion Equation of Fractional Order Using Chebyshev Collocation Method

Ali Shah,

Kamran,

Boulila

et al. 2023

Fractal Fract

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This work presents a highly accurate method for the numerical solution of the advection–diffusion equation of fractional order. In our proposed method, we apply the Laplace transform to handle the time-fractional derivative and utilize the Chebyshev spectral collocation method for spatial discretization. The primary motivation for using the Laplace transform is its ability to avoid the classical time-stepping scheme and overcome the adverse effects of time steps on numerical accuracy and stability. Our method comprises three primary steps: (i) reducing the time-dependent equation to a time-independent equation via the Laplace transform, (ii) employing the Chebyshev spectral collocation method to approximate the solution of the transformed equation, and (iii) numerically inverting the Laplace transform. We discuss the convergence and stability of the method and assess its accuracy and efficiency by solving various problems in two dimensions.

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Section: Introductionmentioning

confidence: 99%

Numerical Solution of Advection–Diffusion Equation of Fractional Order Using Chebyshev Collocation Method

Ali Shah,

Kamran,

Boulila

et al. 2023

Fractal Fract

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“…Several innovative distributions have emerged by leveraging fundamental probabilistic concepts, such as cumulative distribution functions (CDFs) [1][2][3], probability density functions (PDFs), and survival functions. The intention is to introduce enhanced flexibility and encompass a wider spectrum of behaviors compared to the original distributions.…”

Section: Introductionmentioning

confidence: 99%

Toward Enhanced Geological Analysis: A Novel Approach Based on Transmuted Semicircular Distribution

Yedlapalli,

Kishore,

Boulila

et al. 2023

Symmetry

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This paper introduces a novel semicircular distribution obtained by applying the quadratic rank transmutation map to the stereographic semicircular exponential distribution, referred to as the transmuted stereographic semicircular exponential distribution (TSSCED). This newly proposed distribution exhibits enhanced flexibility compared to the baseline stereographic semicircular exponential distribution (SSCEXP). We conduct a comprehensive analysis of the model’s properties and demonstrate its efficacy in data modeling through the application to a real dataset.

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Application of flatlet oblique multiwavelets to solve the fractional stochastic integro‐differential equation using Galerkin method

Irandoust‐Pakchin,

Abdi‐Mazraeh,

Adel

2024

Math Methods in App Sciences

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This study introduces a new numerical approach named flatlet oblique multiwavelets (FOMW) to solve fractional‐order stochastic integro‐differential equation (FSI‐DE). The FOMW is used to create an operational matrix of the stochastic integral, which helps transform the FSI‐DE into a linear system of algebraic equations. This method requires only a small number of basis functions to achieve satisfactory results. The paper also includes a comprehensive discussion on error estimation and convergence analysis, which provides an upper bound of error for the proposed method. Furthermore, numerical experiments have been conducted and compared with other methods, demonstrating the superiority of FOMW in terms of accuracy and efficiency.

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Utilization of Haar wavelet collocation technique for fractal-fractional order problem

Cited by 7 publications

References 18 publications

Numerical Solution of Advection–Diffusion Equation of Fractional Order Using Chebyshev Collocation Method

Numerical Solution of Advection–Diffusion Equation of Fractional Order Using Chebyshev Collocation Method

Toward Enhanced Geological Analysis: A Novel Approach Based on Transmuted Semicircular Distribution

Application of flatlet oblique multiwavelets to solve the fractional stochastic integro‐differential equation using Galerkin method

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