Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method

Khan, Hassan; Farooq, Umar; Shah, Rasool; Băleanu, Dumitru; Arif, Muhammad

doi:10.3390/app10010122

Cited by 36 publications

(20 citation statements)

References 33 publications

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“…In [2], the authors present a new analytical technique based on an innovative transformation in order to solve (2+time fractional-order) dimensional physical models. The proposed method is based on the hybrid methodology of Shehu transformation along with the Adomian decomposition method.…”

Section: Analytical Solutions Of Dimensional Physical Models Using Momentioning

confidence: 99%

Special Issue on Mathematical Modeling Using Differential Equations and Network Theory

Dassios

2020

Applied Sciences

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Section: Analytical Solutions Of Dimensional Physical Models Using Momentioning

confidence: 99%

Special Issue on Mathematical Modeling Using Differential Equations and Network Theory

Dassios

2020

Applied Sciences

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“…To mention a few, we have the homotopy perturbation method (HPM) [6], the Adomian decomposition method (ADM) [7], the Laplace decomposition method (LDM) [8], the homotopy perturbation transform method (HPTM) [9], and so on. Besides using the Laplace-type integral transform [10,11], some new efficient iterative techniques with the Caputo fractional derivative [12] and Atangana-Baleanu fractional derivative [13] are developed, for example, see [14][15][16][17][18][19][20][21][22][23][24][25]. Those iterative algorithms are successfully applied to many applications in applied physical science.…”

Section: Introductionmentioning

confidence: 99%

Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

Maitama¹,

Zhang²

2021

J. Appl. Math. Comput. Mech.

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Using the recently proposed homotopy perturbation Shehu transform method (HPSTM), we successfully construct reliable solutions of some important fractional models arising in applied physical sciences. The nonlinear terms are decomposed using He's polynomials, and the fractional derivative is calculated in the Caputo sense. Using the analytical method, we obtained the exact solution of the fractional diffusion equation, fractional wave equation and the nonlinear fractional gas dynamic equation.

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“…Since then, ADM has been implemented in nonlinear ODEs and PDEs without using perturbation or linearization procedure. e Shehu decomposition method (SDM) is a mixture of ADM and Shehu transform [51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

The Fractional View Analysis of Polytropic Gas, Unsteady Flow System

Khan

Islam

Arif

2021

Mathematical Problems in Engineering

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Generally, the differential equations of integer order do not properly model various phenomena in different areas of science and engineering as compared to differential equations of fractional order. The fractional-order differential equations provide the useful dynamics of the physical system and thus provide the innovative and effective information about the given physical system. Keeping in view the above properties of fractional calculus, the present article is related to the analytical solution of the time-fractional system of equations which describe the unsteady flow of polytropic gas dynamics. The present method provides the series form solution with easily computable components and a higher rate of convergence towards the targeted problem’s exact solution. The present techniques are straightforward and effective for dealing with the solutions of fractional-order problems. The fractional derivatives are expressed in terms of the Caputo operator. The targeted problems’ solutions are calculated using the Adomian decomposition method and variational iteration methods along with Shehu transformation. In the current procedures, we first applied the Shehu transform to reduce the problems into a more straightforward form and then implemented the decomposition and variational iteration methods to achieve the problems’ comprehensive results. The solution of the nonlinear equations of unsteady flow of a polytropic gas at various fractional orders of the derivative is the core point of the present study. The solution of the proposed fractional model is plotted via two- and three-dimensional graphs. It is investigated that each problem’s solution-graphs are best fitted with each other and with the exact solution. The convergence of fractional-order problems can be observed towards the solution of integer-order problems. Less computational time is the major attraction of the suggested methods. The present work will be considered a useful tool to handle the solution of fractional partial differential equations.

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Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method

Cited by 36 publications

References 33 publications

Special Issue on Mathematical Modeling Using Differential Equations and Network Theory

Special Issue on Mathematical Modeling Using Differential Equations and Network Theory

Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

The Fractional View Analysis of Polytropic Gas, Unsteady Flow System

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