A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions

Tripathi, Manoj P.; Baranwal, Vipul K.; Pandey, Ram K.; Singh, Om Prakash

doi:10.1016/j.cnsns.2012.10.014

Cited by 47 publications

(19 citation statements)

References 31 publications

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“…where the (n + 1) × (n + 1) matrix P is called the operational matrix of integration for the generalized generalized hat functions and is given in [32] by: …”

Section: A Brief Review Of the Generalized Hat Functionsmentioning

confidence: 99%

“…The generalized hat basis functions are extension of traditional hat basis functions on the finite interval [0, T ]. A set of these basis functions are usually defined on [0, T ] as [32]:…”

Section: A Brief Review Of the Generalized Hat Functionsmentioning

confidence: 99%

“…Babolian and Mordad [31] have used hat basis function for solving systems of linear and nonlinear integral equations of the second kind by the hat functions. In [32], Tripathi et al have used the generalized hat basis functions to obtain approximate solutions of linear and nonlinear fractional differential equations. In [33], Heydari et al have obtained the operational matrix of stochastic Itô-integration for the generalized hat basis functions, that is:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

Heydari

Hooshmandasl

Cattani

et al. 2015

Journal of Computational Physics

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“…where the (n + 1) × (n + 1) matrix P is called the operational matrix of integration for the generalized generalized hat functions and is given in [32] by: …”

Section: A Brief Review Of the Generalized Hat Functionsmentioning

confidence: 99%

“…The generalized hat basis functions are extension of traditional hat basis functions on the finite interval [0, T ]. A set of these basis functions are usually defined on [0, T ] as [32]:…”

Section: A Brief Review Of the Generalized Hat Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

Heydari

Hooshmandasl

Cattani

et al. 2015

Journal of Computational Physics

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“…Fractional differential equations have also been the focus of many mathematicians. Consequently, considerable attention has been given to their numerical solutions [11], [19], [21], [22], [32], [35]. However, these methods may not be interesting from an engineering approach at least in terms of simulation and implementation of fractional systems.…”

Section: Introductionmentioning

confidence: 99%

New perspectives of analog and digital simulations of fractional order systems

Charef¹,

Charef²,

Djouambi³

et al. 2017

Archives of Control Sciences

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In the recent decades, fractional order systems have been found to be useful in many areas of physics and engineering. Hence, their efficient and accurate analog and digital simulations and numerical calculations have become very important especially in the fields of fractional control, fractional signal processing and fractional system identification. In this article, new analog and digital simulations and numerical calculations perspectives of fractional systems are considered. The main feature of this work is the introduction of an adjustable fractional order structure of the fractional integrator to facilitate and improve the simulations of the fractional order systems as well as the numerical resolution of the linear fractional order differential equations. First, the basic ideas of the proposed adjustable fractional order structure of the fractional integrator are presented. Then, the analog and digital simulations techniques of the fractional order systems and the numerical resolution of the linear fractional order differential equation are exposed. Illustrative examples of each step of this work are presented to show the effectiveness and the efficiency of the proposed fractional order systems analog and digital simulations and implementations techniques.

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“…From the numerical point of view, several methods have been presented to achieve the goal of highly accurate and reliable solutions for the fractional differential equations. The most commonly used methods are fractional differential transform method [21], operational matrix method [22,23], finite difference method [24], and Haar wavelets method [25].…”

Section: Introductionmentioning

confidence: 99%

An Eigenvalue-Eigenvector Method for Solving a System of Fractional Differential Equations with Uncertainty

Shahriyar

Ismail

Aghabeigi

et al. 2013

Mathematical Problems in Engineering

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A new method is proposed for solving systems of fuzzy fractional differential equations (SFFDEs) with fuzzy initial conditions involving fuzzy Caputo differentiability. For this purpose, three cases are introduced based on the eigenvalue-eigenvector approach; then it is shown that the solution of system of fuzzy fractional differential equations is vector of fuzzy-valued functions. Then the method is validated by solving several examples.

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A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions

Cited by 47 publications

References 31 publications

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

New perspectives of analog and digital simulations of fractional order systems

An Eigenvalue-Eigenvector Method for Solving a System of Fractional Differential Equations with Uncertainty

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