New approach to approximate the solution for the system of fractional order Volterra integro-differential equations

Akbar, M. Ali; Nawaz, Rashid; Ahsan, Sumbal; Nisar, Kottakkaran Sooppy; Abdel‐Aty, Abdel‐Haleem; Eleuch, Hichem

doi:10.1016/j.rinp.2020.103453

Cited by 25 publications

(7 citation statements)

References 39 publications

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“…However, in this case, the accuracy of our method will be lower compared to when the Gram-Schmidt process is eliminated. In this article, we compared the present method to the extension of optimal homotopy asymptotic method and Block-Pulse functions [1,4]. All the numerical results show that the current method is very efficient.…”

Section: Introductionmentioning

confidence: 97%

“…Fractional calculations, in the form of integral, derivative, and integral-derivative operators, are utilized in various fields such as fractional dynamics, mechanics of solids, visco-elastically damped structures, nonlinear oscillation, bio-engineering, and continuum mechanics [1]. Numerous numerical methods have been developed to solve linear and non-linear systems of fractional-order Volterra integro-differential equations, including the optimal homotopy asymptotic method, Block-Pulse functions, wavelets method, Legendre wavelets method, and Haar wavelet method [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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A new application of the reproducing kernel method for solving linear systems of fractional order Volterra integro-differential equations

Amoozad,

Abbasbandy,

Sahihi

et al. 2024

Phys. Scr.

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In this article, a new implementation of the reproducing kernel method is presented for solving systems of fractional-order Volterra integro-differential equations. Unlike previous implementations, this method does not rely on the Gram-Schmidt process. The reproducing kernel method utilizes various components, including space, inner product, bases, and points. Furthermore, the system of fractional-order Volterra integro-differential equations involves Caputo's fractional derivative and Volterra integral. However, when using the reproducing kernel method to solve these systems, challenges such as longer execution time and lower accuracy may arise compared to other methods. The present method has overcome these challenges with features such as easy implementation, high accuracy, and lower execution time.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

A new application of the reproducing kernel method for solving linear systems of fractional order Volterra integro-differential equations

Amoozad,

Abbasbandy,

Sahihi

et al. 2024

Phys. Scr.

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“…Other than previous methods, we present Tau monic Laguerre method based on operational matrix for solving systems of FIDEs. let's consider the following system of FIDEs [28]:…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of systems of fractional order integro-differential equations with a Tau method based on monic Laguerre polynomials

Masoud

2022

J. Math. Anal. Model.

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In this paper, numerical technique based on monic Laguerre polynomials is proposed to obtain approximate solutions of initial value problems for systems of fractional order integro-differential equations (FIDEs). Operational fractional integral matrix is constructed. This operational matrix is applied together with the monic Laguerre Tau method to solve systems of FIDEs. This systems of FIDEs will be transformed into a system of algebraic equations which can be solved easily. Numerical results and comparisons with other methods are also presented to show the efficiency and applicability of the proposed method.

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“…For example a temperature-heat flux relationship for heat flow in semi-infinite conductor is presented in [1], the beam heating problem is given in [3]. Theoretical analysis of fractional thermal equation is given, e.g., in [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Model of the Two Dimensional Heat Transfer Process

Oprzędkiewicz¹,

Mitkowski²,

Rosół³

2021

Energies

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In this paper, a new, state space, fractional order model of a heat transfer in two dimensional plate is addressed. The proposed model derives directly from a two dimensional heat transfer equation. It employes the Caputo operator to express the fractional order differences along time. The spectrum decomposition and stability of the model are analysed. The formulae of impluse and step responses of the model are proved. Theoretical results are verified using experimental data from thermal camera. Comparison model vs experiment shows that the proposed fractional model is more accurate in the sense of MSE cost function than integer order model.

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New approach to approximate the solution for the system of fractional order Volterra integro-differential equations

Cited by 25 publications

References 39 publications

A new application of the reproducing kernel method for solving linear systems of fractional order Volterra integro-differential equations

A new application of the reproducing kernel method for solving linear systems of fractional order Volterra integro-differential equations

Numerical solution of systems of fractional order integro-differential equations with a Tau method based on monic Laguerre polynomials

Fractional Order Model of the Two Dimensional Heat Transfer Process

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