Analytical Approach for the Approximate Solution of Harry Dym Equation with Caputo Fractional Derivative

Nadeem, Muhammad; Li, Zitian; Alsayaad, Yahya

doi:10.1155/2022/4360735

Cited by 8 publications

(4 citation statements)

References 28 publications

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“…(3) Defnition 4. [54] Te Mohand transform M in the presence of Caputo fractional derivative (3) can be written as follows:…”

Section: Preliminariesmentioning

confidence: 99%

Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

Qayyum,

Ahmad,

Tahir

et al. 2023

International Journal of Intelligent Systems

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This paper contains modeling of a fuzzy-fractional financial chaotic model based on triangular fuzzy numbers (TFNs) to predict the idea that long-term dependency and uncertainty both have an impact on the financial market. For solution purposes, the He–Mohand algorithm is proposed where homotopy perturbation is hybrid with Mohand transform in a fuzzy-Caputo sense. In analysis, solutions and corresponding errors at upper and lower bounds are estimated. The obtained numerical results are displayed in tables to show the reliability and efficiency of the proposed methodology. Upper bound errors range from 10 − 6 to 10 − 12 and lower bound errors from 10 − 6 to 10 − 11 . For graphical analysis, system profiles are illustrated as two-dimensional and three-dimensional plots at diverse values of fractional parameters and time to comprehend the physical behavior of the proposed fuzzy-fractional model. These plots demonstrate that the interest rate, price index, and investment demand decrease with the increase of the value of the r -cut at the lower bound. At the upper bound, this behavior is totally opposite. The chaotic behavior of the system at smaller values of saving rate, elasticity of demands, and per-investment cost is greater in contrast to their larger value. Analysis reveals that the proposed methodology (He–Mohand algorithm) provides a new way of understanding the complicated structure of financial systems and provides new insights into the dynamics of financial markets. This algorithm has potential applications in risk management, portfolio optimization, and trading strategies.

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“…(3) Defnition 4. [54] Te Mohand transform M in the presence of Caputo fractional derivative (3) can be written as follows:…”

Section: Preliminariesmentioning

confidence: 99%

Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

Qayyum,

Ahmad,

Tahir

et al. 2023

International Journal of Intelligent Systems

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“…The nonlinear time fractional Harry Dym equation is given by [14] D α t u(x, t) = u 3 (x, t)u xxx (x, t), 0 < α ≤ 1,…”

Section: Introductionmentioning

confidence: 99%

Soliton Solution of the Nonlinear Time Fractional Equations: Comprehensive Methods to Solve Physical Models

O’Regan,

Aderyani,

Saadati

et al. 2024

Axioms

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In this paper, we apply two different methods, namely, the G′G-expansion method and the G′G2-expansion method to investigate the nonlinear time fractional Harry Dym equation in the Caputo sense and the symmetric regularized long wave equation in the conformable sense. The mentioned nonlinear partial differential equations (NPDEs) arise in diverse physical applications such as ion sound waves in plasma and waves on shallow water surfaces. There exist multiple wave solutions to many NPDEs and researchers are interested in analytical approaches to obtain these multiple wave solutions. The multi-exp-function method (MEFM) formulates a solution algorithm for calculating multiple wave solutions to NPDEs and at the end of paper, we apply the MEFM for calculating multiple wave solutions to the (2 + 1)-dimensional equation.

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“…The nonlinear time fractional Harry Dym equation is given by [6] D α t u(x, t) = u 3 (x, t)u xxx (x, t), 0 < α ≤ 1, (1.1)…”

Section: Introductionmentioning

confidence: 99%

Soliton Solutions of the Nonlinear Time Fractional Harry Dym Equation in the Caputo Sense and the Symmetric Regularized Long Wave Equation in the Conformable Sense

Aderyani

Saadati

O’Regan

et al. 2023

Preprint

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In this paper, we apply two different methods, namely, the G G-expansion method and G G 2-expansion method to investigate the nonlinear time fractional Harry Dym equation in the Caputo sense and the symmetric regularized long wave equation in the conformable sense. The mentioned NPDES arise in diverse physical applications like ion sound waves in plasma and waves on shallow water surfaces. There exist multiple wave solutions to many NPDEs and one is interested in analytical approaches for obtaining multiple wave solutions to NPDEs. The multi-exp-function method formulates a solution algorithm for calculating multiple wave solutions to NPDEs and at the end of paper, we apply the MEFM for calculating multiple wave solutions to the (2+1)-dimensional equation.

show abstract

Analytical Approach for the Approximate Solution of Harry Dym Equation with Caputo Fractional Derivative

Cited by 8 publications

References 28 publications

Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

Soliton Solution of the Nonlinear Time Fractional Equations: Comprehensive Methods to Solve Physical Models

Soliton Solutions of the Nonlinear Time Fractional Harry Dym Equation in the Caputo Sense and the Symmetric Regularized Long Wave Equation in the Conformable Sense

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