Fractional Reduced Differential Transform Method for Space-Time Fractional Order Heat-Like and Wave-Like Partial Differential Equations

Lu, Dianchen; Wang, Jun; Arshad, Muhammad; Abdullah, .; Ali, Asghar

doi:10.1166/jap.2017.1383

Cited by 11 publications

(6 citation statements)

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“…Definition 4 (see [33,34]). If w(x, y, z, t) is analytic and continuously differentiable with respect to space variables x, y, and time variable t in the domain of interest, then the spectrum function is defined as…”

Section: Fractional Reduced Differential Transform Methods (Frdtm)mentioning

confidence: 99%

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Three-Dimensional Fourth-Order Time-Fractional Parabolic Partial Differential Equations and Their Analytical Solution

Mussa

Gizaw

Negassa

2021

Mathematical Problems in Engineering

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In this study, the fractional reduced differential transform method (FRDTM) is employed to solve three-dimensional fourth-order time-fractional parabolic partial differential equations with variable coefficients. The fractional derivative used in this study is in the Caputo sense. A few important lemmas which are essential to solve the problems using the proposed method are proved. The novelty of this method is that it uses appropriate initial conditions and finds the solution to the problems without any discretization, linearization, perturbation, or any restrictive assumptions. Two numerical examples are considered in order to validate the efficiency and reliability of the method. Furthermore, the FRDTM solution when α = 1 is compared with other analytical methods available in the existing literature. Computational results are shown in tables and graphs. The obtained results revealed that the method is capable and simple to solve fractional partial differential equations. The software used for the calculations in this study is Mathematica 7.

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Section: Fractional Reduced Differential Transform Methods (Frdtm)mentioning

confidence: 99%

“…In this section, some basic definitions and lemmas associated with fractional calculus are presented. Some of these definitions are due to Riemann-Liouville and Caputo sense; for details, see [2,24,[30][31][32][33].…”

Section: Fractional Calculusmentioning

confidence: 99%

Three-Dimensional Fourth-Order Time-Fractional Parabolic Partial Differential Equations and Their Analytical Solution

Mussa

Gizaw

Negassa

2021

Mathematical Problems in Engineering

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“…Table 1 represents selected properties of FRDTM, the proofs of these properties can be found in [40,[46][47][48], wherever δða − bÞ is…”

Section: Frdtm For 3 Variablesmentioning

confidence: 99%

Exact Solutions of the 3D Fractional Helmholtz Equation by Fractional Differential Transform Method

Alshammari

Abuasad

2022

Journal of Function Spaces

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In this work, we applied the fractional reduced differential transform method (FRDTM) to find the exact solutions of the three-dimensional fractional Helmholtz equation (FHE) and compared our outcomes with the tenth-order approximate solutions for diverse fractional orders. Different values of fractional derivatives are signified explicitly in three dimensions. Outcomes are denoted in the tables for nonfractional exact and approximate solutions and fractional approximate solutions for different fractional orders. Two examples are given to prove the proficiency of the suggested method, to resolve diverse categories of fractional partial differential equations.

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“…Jumarie applied the fractional Taylor formula to solve time and space fractional Black-Scholes equation and derived the optimal fractional Merton's portfolio [23]. The numerical solution of various heat and wave partial differential equations have been obtained through fractional reduced diferential transform method (FRDTM) [26].…”

Section: Introductionmentioning

confidence: 99%

A fractional reduced differential transform method for solving time fractional Black Scholes American option pricing equation

Ahmad

Mishra²,

Jain

2021

CMI

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In this paper, fractional reduced differential transform method (FRDTM) is operated to solve time fractional Black-Scholes American option pricing equation paying no dividends.The Black-Scholes model plays a significant role in the evaluation of European or American call and put options. The advantage of the proposed method to other existing methods is that it finds the solution without discretization or transformation. While using this method, no recommended assumptions are needed and hence the computational work reduces to a greater extent. Numerical experiments prove that the proposed method is efficient and valid for obtaining the solution of time fractional Black-Scholes equation governing American options. This method proves to be powerful for solving general fractional order partial differential equations (PDEs) existing in the field of Science, Engineering and other related fields.

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Fractional Reduced Differential Transform Method for Space-Time Fractional Order Heat-Like and Wave-Like Partial Differential Equations

Cited by 11 publications

References 0 publications

Three-Dimensional Fourth-Order Time-Fractional Parabolic Partial Differential Equations and Their Analytical Solution

Three-Dimensional Fourth-Order Time-Fractional Parabolic Partial Differential Equations and Their Analytical Solution

Exact Solutions of the 3D Fractional Helmholtz Equation by Fractional Differential Transform Method

A fractional reduced differential transform method for solving time fractional Black Scholes American option pricing equation

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