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

Noor, Saima; Alshehry, Azzh Saad; Aljahdaly, Noufe H.; Dutt, Hina M.; Khan, Imran; Shah, Rasool

doi:10.3390/sym15040881

Cited by 5 publications

(1 citation statement)

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“…Regarding the theoretical and numerical findings for the stochastic wave equation, we recommend exploring references such as [18][19][20][21]. For theoretical advancements in fractional-order nonlinear differential equations, recent works such as [22][23][24][25][26][27] and their references provide a comprehensive overview.…”

Section: Introductionmentioning

confidence: 99%

Galerkin Finite Element Approximation of a Stochastic Semilinear Fractional Wave Equation Driven by Fractionally Integrated Additive Noise

Egwu

Yan

2023

Foundations

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We investigate the application of the Galerkin finite element method to approximate a stochastic semilinear space–time fractional wave equation. The equation is driven by integrated additive noise, and the time fractional order α∈(1,2). The existence of a unique solution of the problem is proved by using the Banach fixed point theorem, and the spatial and temporal regularities of the solution are established. The noise is approximated with the piecewise constant function in time in order to obtain a stochastic regularized semilinear space–time wave equation which is then approximated using the Galerkin finite element method. The optimal error estimates are proved based on the various smoothing properties of the Mittag–Leffler functions. Numerical examples are provided to demonstrate the consistency between the theoretical findings and the obtained numerical results.

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Section: Introductionmentioning

confidence: 99%

Galerkin Finite Element Approximation of a Stochastic Semilinear Fractional Wave Equation Driven by Fractionally Integrated Additive Noise

Egwu

Yan

2023

Foundations

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Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems

Ganie,

Noor,

Al Huwayz

et al. 2024

Open Physics

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In this investigation, the fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) problem is solved using two modern semi-analytic techniques known as the Aboodh residual power series method (ARPSM) and Aboodh transform iteration method (ATIM). The two suggested approaches are briefly explained, along with how to use them to solve the fractional Hirota–Satsuma coupled KdV problem. Some analytical approximate solutions for the current problem are derived using the proposed techniques until the second-order approximation. To ensure high accuracy of the derived approximation, they are analyzed numerically and graphically and compared with the exact solutions of the integer cases. The offered techniques demonstrate more accuracy in their outcomes compared to other alternatives. The numerical results show that ARPSM and ATIM are highly accurate, practical, and beneficial for solving nonlinear equation systems. The current results are expected to help many physics researchers in modeling their different physical problems, especially those interested in plasma physics.

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Iterative solution of the fractional Wu-Zhang equation under Caputo derivative operator

Yasmin,

Alderremy,

Shah

et al. 2024

Front. Phys.

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In this study, we employ the effective iterative method to address the fractional Wu-Zhang Equation within the framework of the Caputo Derivative. The effective iterative method offers a practical approach to obtaining approximate solutions for fractional differential equations. We seek to provide insights into its solution and behavior by applying this method to the Wu-Zhang Equation. Through numerical analysis and the presentation of relevant tables and Figures, we demonstrate the accuracy and efficiency of this method in solving the fractional Wu-Zhang Equation. This research contributes to the understanding and solution of fractional-order differential equations and their applications in various scientific and engineering domains.

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

Cited by 5 publications

References 50 publications

Galerkin Finite Element Approximation of a Stochastic Semilinear Fractional Wave Equation Driven by Fractionally Integrated Additive Noise

Galerkin Finite Element Approximation of a Stochastic Semilinear Fractional Wave Equation Driven by Fractionally Integrated Additive Noise

Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems

Iterative solution of the fractional Wu-Zhang equation under Caputo derivative operator

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