Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

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A Local Fractional Derivative

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2003/vib-48385 ◽

2003 ◽

Cited By ~ 1

Author(s):

Xiaorang Li ◽

Christopher Essex ◽

Matt Davison

Keyword(s):

Fractional Derivative ◽

Fractional Order ◽

Local Property ◽

Order Derivative ◽

Fractional Order Derivative ◽

Local Fractional Derivative ◽

Basic Properties ◽

Differentiable Functions ◽

Definition Of

A new definition of fractional order derivative is given and its basic properties are investigated. This definition is based on the Weyl derivative and is a local property of functions. It can be applied to non-differentiable functions and may be useful for studying fractal curves.

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A Numerical Method for Calculating Fractional Derivative

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.775.426 ◽

2015 ◽

Vol 775 ◽

pp. 426-430

Author(s):

Jun Huang ◽

Yong Jun Li ◽

Fan Huang

Keyword(s):

Fractional Derivative ◽

Numerical Method ◽

Fractional Order ◽

High Precision ◽

Good Stability ◽

Order Derivative ◽

Singularity Problem ◽

Numerical Examples ◽

Fractional Order Derivative

A numerical method is proposed for calculating the fractional order derivative and successfully resolving the integrand singularity problem based on Zhang-Shimizu algorithm. And then a method is developed to calculate the twice nonlinear fractional derivative, numerical examples demonstrate the numerical method with high precision and good stability.

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A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

Journal of Function Spaces ◽

10.1155/2021/1273405 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Hakimeh Mohammadi ◽

Mohammed K. A. Kaabar ◽

Jehad Alzabut ◽

A. George Maria Selvam ◽

Shahram Rezapour

Keyword(s):

Fractional Derivative ◽

Fractional Order ◽

Fixed Point Theory ◽

Equilibrium Points ◽

Hemorrhagic Fever ◽

Order Derivative ◽

Common Disease ◽

Fractional Order Derivative ◽

Crimean Congo Hemorrhagic Fever ◽

Caputo Fractional Order Derivative

Crimean-Congo hemorrhagic fever is a common disease between humans and animals that is transmitted to humans through infected ticks, contact with infected animals, and infected humans. In this paper, we present a boxed model for the transmission of Crimean-Congo fever virus. With the help of the fixed-point theory, our proposed system model is investigated in detail to prove its unique solution. Given that the Caputo fractional-order derivative preserves the system’s historical memory, we use this fractional derivative in our modeling. The equilibrium points of the proposed system and their stability conditions are determined. Using the Euler method for the Caputo fractional-order derivative, we calculate the approximate solutions of the fractional system, and then, we present a numerical simulation for the transmission of Crimean-Congo hemorrhagic fever.

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Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative

Discrete Dynamics in Nature and Society ◽

10.1155/2020/8047347 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Ndolane Sene ◽

Babacar Sène ◽

Seydou Nourou Ndiaye ◽

Awa Traoré

Keyword(s):

Analytical Solution ◽

Fractional Derivative ◽

Fractional Order ◽

Numerical Scheme ◽

Fractional Derivatives ◽

Fractional Integration ◽

Order Derivative ◽

Graphical Representations ◽

Fractional Order Derivative ◽

Black Scholes

The value of an option plays an important role in finance. In this paper, we use the Black–Scholes equation, which is described by the nonsingular fractional-order derivative, to determine the value of an option. We propose both a numerical scheme and an analytical solution. Recent studies in fractional calculus have included new fractional derivatives with exponential kernels and Mittag-Leffler kernels. These derivatives have been found to be applicable in many real-world problems. As fractional derivatives without nonsingular kernels, we use a Caputo–Fabrizio fractional derivative and a Mittag-Leffler fractional derivative. Furthermore, we use the Adams–Bashforth numerical scheme and fractional integration to obtain the numerical scheme and the analytical solution, and we provide graphical representations to illustrate these methods. The graphical representations prove that the Adams–Bashforth approach is helpful in getting the approximate solution for the fractional Black–Scholes equation. Finally, we investigate the volatility of the proposed model and discuss the use of the model in finance. We mainly notice in our results that the fractional-order derivative plays a regulator role in the diffusion process of the Black–Scholes equation.

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GENERALIZED THEORY OF MAGNETO-THERMO-VISCOELASTIC SPHERICAL CAVITY PROBLEM UNDER FRACTIONAL ORDER DERIVATIVE: STATE SPACE APPROACH

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.11.86 ◽

2020 ◽

Vol 9 (11) ◽

pp. 9769-9780

Author(s):

S.G. Khavale ◽

K.R. Gaikwad

Keyword(s):

State Space ◽

Fractional Order ◽

Order Derivative ◽

Laplace Inversion ◽

State Space Approach ◽

Spherical Region ◽

Fractional Order Derivative ◽

Numerical Laplace Inversion ◽

Mathcad Software ◽

Space Approach

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

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