Application of residual power series method to time fractional gas dynamics equations

Rao, T. R. Ramesh

doi:10.1088/1742-6596/1139/1/012007

Cited by 5 publications

(2 citation statements)

References 8 publications

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“…Furthermore, RPSM can be implemented directly into the present equation by choosing an initial guess approximation. In literature, RPSM has been used to find power series solutions for different problems, such as those provided in [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44].…”

Section: 𝐷 𝑡mentioning

confidence: 99%

Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method

ÇULHA ÜNAL

2023

Journal of New Theory

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One of the prominent nonlinear partial differential equations in mathematical physics is the Clannish Random Walker’s Parabolic (CRWP) equation. This study uses Residual Power Series Method (RPSM) to solve the time fractional CRWP equation. In this equation, the fractional derivatives are considered in Caputo’s sense. The effectiveness of RPSM is illustrated with graphical results. The series solutions are utilized to represent the approximate solutions. Besides, the approximate solutions found by the suggested method ensure good accuracy when compared with the exact solution. Moreover, RPSM efficiently analyzes complex problems that emerge in the related mathematical and scientific fields.

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Section: 𝐷 𝑡mentioning

confidence: 99%

Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method

ÇULHA ÜNAL

2023

Journal of New Theory

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“…RPSM method have been used by several authors in various fields, such as Boussinesq–Burgers equations [16], fractional diffusion equations [14], fuzzy differential equations [1], fractional Burger types equations [13], time‐fractional Fokker–Planck equations [20], time fractional nonlinear coupled Boussinesq–Burgers equations [15], nonlinear fractional KdV–Burgers equation [6], higher order initial value problems [2], for linear and nonlinear Lane–Emden equations [3], system of multipantograph differential equations [12], system of Fredhlom integral equations [11], time fractional Whitham–Broer–Kaup equations [19]], time fractional nonlinear gas dynamics equations [18], and is used for time fractional model of vibration equation [8]. Modeling and analysis of fractal‐fractional partial differential equations for application to reaction–diffusion model [17] and analytic approximate solutions of diffusion equations arising in oil pollution have been studied [4].…”

Section: Introductionmentioning

confidence: 99%

A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions

Modanlı

Abdulazeez

Husien

2020

Numerical Methods Partial

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This article will give the residual power series method (RPSM) for solving pseudo hyperbolic partial differential equations with nonlocal conditions, RPSM is essentially based on general formula of Taylor series with residual error function. A new analytical solution is investigated. The analytical solution is designed to find the approximation solutions by RPSM and compare the obtained results from the current method with the exact solution that detects the precision, reliability, and rapid convergence of the proposed method. Finally at different times through the graphical representation of obtained results are given.

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The solutions of nonlinear fractional partial differential equations by using a novel technique

Alderremy

Khan

et al. 2022

Open Physics

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In this article, the solutions of higher nonlinear partial differential equations (PDEs) with the Caputo operator are presented. The fractional PDEs are modern tools to model various phenomena more accurately. The residual power series method (RPSM) is used for the solution analysis of fractional partial differential equations (FPDEs), which has direct implementation for the solutions of fractional partial differential equations. In this work, the solutions to a few nonlinear FPDEs are handled by the proposed technique. The general and particular schemes of RPSM are constructed and implemented successfully. The fractional solutions of PDEs have provided many useful dynamics of the targeted problems. The RPSM results for both integer and fractional-order FPDEs are further explained and elaborated by using graphs and tables. It is observed that the higher accuracy of RPSM is achieved with fewer calculations. Graphs and tables for fractional-order solutions are presented, which confirm the convergence phenomena of fractional solutions toward integer order solutions of each problem. The suggested method can be extended to the solutions of other nonlinear fractional partial differential equations.

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Application of residual power series method to time fractional gas dynamics equations

Cited by 5 publications

References 8 publications

Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method

Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method

A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions

The solutions of nonlinear fractional partial differential equations by using a novel technique

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