An Analytical Technique Implemented in the Fractional Clannish Random Walker’s Parabolic Equation with Nonlinear Physical Phenomena

Alam, Md. Nur; Talib, Imran; Bazighifan, Omar; Chalishajar, Dimplekumar; Almarri, Barakah

doi:10.3390/math9080801

Cited by 15 publications

(5 citation statements)

References 30 publications

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“…In the literature, there are a few approaches that are commonly used for obtaining exact solutions to the integrable wave equation (1), adapted (G/G)-expansion scheme [43], modified extended auxiliary equation mapping [44] modified F expansion method [45]. Compared to the current analytical technique, the proposed method is more dependable and computationally efficient.…”

Section: Introductionmentioning

confidence: 99%

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Asjad¹,

Ashaq²,

Faridi³

et al. 2023

Preprint

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In this article, the new extended direct algebraic method is used to build the exact travellingwave solutions for the non-linear time-fractional Clannish Random Walker’s Parabolic equation.This study establishes the framework in which periodic, singular, dark, bright and kink-typewave solitons are obtained with exact solutions offered by the mixed hyperbolic and trigonom-etry solutions, mixed periodic and periodic solutions, plane solutions, shock solutions, mixedtrigonometric solutions, mixed singular solutions, mixed shock single solutions, complex solitarysingular solutions, shock solutions and shock wave solutions. The exact soliton solutions of thetime-fractional clannish random walker’s parabolic equation model is graphically presented atdifferent values of involved parameters by Wolfram Mathematica software. The propagating behaviours display in 3-D, contour and 2-D surfaces of the obtained results to visualise the im-pact of the involved parameters. The sensitivity analysis is demonstrated for the wave profilesof the designed dynamical framed structure, where the soliton wave number parameter regulatesthe water wave singularity. This analysis illustrates that the utilized method is efficient andreliable and can be useful to find appropriate solutions in closed-form solitary soliton to a wide range of non-linear evolution equations. These techniques can also be utilised to find new exact travelling wave solutions for any class of integer or fractional differential equations thatarise in mathematical physics.

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Section: Introductionmentioning

confidence: 99%

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Asjad¹,

Ashaq²,

Faridi³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…9 Alam et al executed to obtain exact solutions to the fractional Clannish Random Walker's Parabolic (FCRWP) equation, and it could also be used to acquire exact solutions for other nonlinear fractional mathematical models (NLFMMs). 10 Elbeleze et al combined the homotopy perturbation method (HPM), Sumudu transform, and He's polynomials and proposed an asymptotic analytical method for FBS model using Sumudu transform. 11 Song and Wang solved the European and American put option pricing models that combine the time-FBS equation with the conditions satisfied by the standard put options by using the implicit scheme of the finite difference method.…”

Section: Introductionmentioning

confidence: 99%

“…Kumar et al dealt with a fractional extension of the vibration equation for very large membranes with distinct special cases 9 . Alam et al executed to obtain exact solutions to the fractional Clannish Random Walker's Parabolic (FCRWP) equation, and it could also be used to acquire exact solutions for other nonlinear fractional mathematical models (NLFMMs) 10 . Elbeleze et al combined the homotopy perturbation method (HPM), Sumudu transform, and He's polynomials and proposed an asymptotic analytical method for FBS model using Sumudu transform 11 .…”

Section: Introductionmentioning

confidence: 99%

Haar wavelet transform and variational iteration method for fractional option pricing models

Liu

Meng

Xing

et al. 2022

Math Methods in App Sciences

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Comparing with the linear Black-Scholes model, the fractional option pricing models are constructed by taking account some more parameters like, for example, the transaction cost, so that it becomes more difficult to find the exact analytical solution. In this paper, we analyze a nonlinear fractional Black and Scholes model, and we find the solution by using a novel numerical method, based on a mixture of efficient techniques. In particular, we combine (1) Haar wavelet integration method which transforms the PDEs into a system of algebraic equations, (2) the homotopy perturbation method in order to linearize the problem, and (3) the variational iteration method which will be used to solve the large system of algebraic equations efficiently. We will also show that, in comparison with other popular methods, our coupling technique has a higher efficiency and calculation precision.

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“…As a result, fractional-order differential operators are widely used to solve systems by developing more accurate models [1][2][3][4]. The nonlocal property of the fractional-order operators makes them more efficient for modeling the various problems of physics, fluid dynamics and their related disciplines [1,[5][6][7][8][9]. For example, consider a thin rigid plate of mass a 1 and area R immersed in a Newtonian fluid of infinite extent and connected by a massless spring of stiffness K to a fixed point.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Caputo Fractional-Order Differential Equations by Developing New Operational Matrices of Vieta–Lucas Polynomials

et al. 2022

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In this article, we develop a numerical method based on the operational matrices of shifted Vieta–Lucas polynomials (VLPs) for solving Caputo fractional-order differential equations (FDEs). We derive a new operational matrix of the fractional-order derivatives in the Caputo sense, which is then used with spectral tau and spectral collocation methods to reduce the FDEs to a system of algebraic equations. Several numerical examples are given to show the accuracy of this method. These examples show that the obtained results have good agreement with the analytical solutions in both linear and non-linear FDEs. In addition to this, the numerical results obtained by using our method are compared with the numerical results obtained otherwise in the literature.

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An Analytical Technique Implemented in the Fractional Clannish Random Walker’s Parabolic Equation with Nonlinear Physical Phenomena

Cited by 15 publications

References 30 publications

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Haar wavelet transform and variational iteration method for fractional option pricing models

Numerical Study of Caputo Fractional-Order Differential Equations by Developing New Operational Matrices of Vieta–Lucas Polynomials

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