A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas

Al-Sawalha, M. Mossa; Agarwal, Ravi P.; Shah, Rasool; Ababneh, Osama Y.; Weera, Wajaree

doi:10.3390/math10132293

Cited by 15 publications

(3 citation statements)

References 48 publications

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“…Thirdly, the residual power series method does not suffers from mathematical rounds error and does not consume significant time or memory. Fourthly, it can be immediately used to the proposed model by selecting an appropriates starting condition approximations, without requiring any conversion when transitioning from lower to higher orders (Al-Khaled & Abu Arqub, 2017; El-Kalla et al, 2021) [60][61][62]. In this paper, we utilize the Laplace RPSM (LRPSM) to obtain a precise solutions for nonlinear fractional PDEs.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System

et al. 2023

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In this article, we present a modified strategy that combines the residual power series method with the Laplace transformation and a novel iterative technique for generating a series solution to the fractional nonlinear Belousov–Zhabotinsky (BZ) system. The proposed techniques use the Laurent series in their development. The new procedures’ advantages include the accuracy and speed in obtaining exact/approximate solutions. The suggested approach examines the fractional nonlinear BZ system that describes flow motion in a pipe.

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Section: Introductionmentioning

confidence: 99%

A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System

et al. 2023

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“…Thirdly, it does not suffer from computational rounding errors and does not require much time or memory [48][49][50]. Lastly, the RPSM can be directly applied to a specific issue by selecting a suitable initial approximation and does not necessitate any transformations when shifting from low-order to high-order or from simple linearity to complex non-linearity [51][52][53].…”

Section: Introductionmentioning

confidence: 99%

Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics

et al. 2023

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In this paper, we investigate the fractional-order Klein–Fock–Gordon equations on quantum dynamics using a new iterative method and residual power series method based on the Caputo operator. The fractional-order Klein–Fock–Gordon equation is a generalization of the traditional Klein–Fock–Gordon equation that allows for non-integer orders of differentiation. This equation has been used in the study of quantum dynamics to model the behavior of particles with fractional spin. The Laplace transform is employed to transform the equations into a simpler form, and the resulting equations are then solved using the proposed methods. The accuracy and efficiency of the method are demonstrated through numerical simulations, which show that the method is superior to existing numerical methods in terms of accuracy and computational time. The proposed method is applicable to a wide range of fractional-order differential equations, and it is expected to find applications in various areas of science and engineering.

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“…The ADE is used in the study of solute transport or Brownian motion of particles in a fluid that occurs when advection and particle dispersion occur at the same time [20,21]. The fractional advection-dispersion equation better represents the phenomenon of anomalous particle diffusion in the transport process; in anomalous diffusion, solute transport is faster or faster than the time's inferred square root given by Baeumer et al [22].…”

Section: Introductionmentioning

confidence: 99%

A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods

Aljahdaly

Shah

Naeem

et al. 2022

Journal of Function Spaces

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The approximate solutions of the time fractional advection-dispersion equation are presented in this article. The nonlocal nature of solute movement and the nonuniformity of fluid flow velocity in the advection-dispersion process lead to the formation of a heterogeneous system, which can be modeled using a fractional advection-dispersion equation, which generalizes the classical advection-dispersion equation and replaces the time derivative with the fractional Caputo derivative. Researchers use a variety of numerical techniques to study such fractional models, but the nonlocality of the derivative having fractional order leads to high computation complexity and complex calculations, so the task is to find an efficient technique that requires less computation and provides greater accuracy when numerically solving such models. A innovative techniques, homotopy perturbation method and new iteration method, are used in connection with the Elzaki transform to solve the “fractional advection-dispersion equation” which provides the solution in the convergent series form. When the homotopy perturbation method is used with the Elzaki transform, fast convergent series solutions can be obtained with less computation. By solving some cases of time-fractional advection-dispersion equation with varied initial conditions with the help of new iterative transform method and homotopy perturbation transform method demonstrates the usefulness of the proposed methods.

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A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas

Cited by 15 publications

References 48 publications

A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System

A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System

Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics

A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods

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