Finite Difference Method with Metaheuristic Orientation for Exploration of Time Fractional Partial Differential Equations

Khan, Najeeb Alam; Ahmed, Samreen

doi:10.1007/s40819-021-01061-y

Int. J. Appl. Comput. Math

2021

DOI: 10.1007/s40819-021-01061-y

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Finite Difference Method with Metaheuristic Orientation for Exploration of Time Fractional Partial Differential Equations

Najeeb Alam Khan

Samreen Ahmed

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2022

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Cited by 3 publications

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The exact solutions of the conformable time fractional version of the generalized Pochhammer–Chree equation

Nuwairan

2022

Math Sci

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The time-fractional version of the generalized Pochhammer–Chree equation is analyzed. In this paper, the equation is converted into an ordinary differential equation by applying certain real transformation, then the discrimination of polynomials system is used to find exact solutions depending on the fractional order derivative. The obtained solutions are graphically illustrated for different values of the fractional order derivative keeping the other parameters fixed.

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The exact solutions of the conformable time fractional version of the generalized Pochhammer–Chree equation

Nuwairan

2022

Math Sci

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A spectral collocation method based on fractional Pell functions for solving time–fractional Black–Scholes option pricing model

Taghipour

Aminikhah

2022

Chaos, Solitons & Fractals

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An efficient modified hybrid explicit group iterative method for the time-fractional diffusion equation in two space dimensions

Salama¹,

Hamid²,

Ali³

et al. 2022

MATH

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<abstract><p>In this paper, a new modified hybrid explicit group (MHEG) iterative method is presented for the efficient and accurate numerical solution of a time-fractional diffusion equation in two space dimensions. The time fractional derivative is defined in the Caputo sense. In the proposed method, a Laplace transformation is used in the temporal domain, and, for the spatial discretization, a new finite difference scheme based on grouping strategy is considered. The unique solvability, unconditional stability and convergence are thoroughly proved by the matrix analysis method. Comparison of numerical results with analytical and other approximate solutions indicates the viability and efficiency of the proposed algorithm.</p></abstract>

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Finite Difference Method with Metaheuristic Orientation for Exploration of Time Fractional Partial Differential Equations

Cited by 3 publications

References 34 publications

The exact solutions of the conformable time fractional version of the generalized Pochhammer–Chree equation

The exact solutions of the conformable time fractional version of the generalized Pochhammer–Chree equation

A spectral collocation method based on fractional Pell functions for solving time–fractional Black–Scholes option pricing model

An efficient modified hybrid explicit group iterative method for the time-fractional diffusion equation in two space dimensions

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