scholarly journals Generalized Hukuhara Conformable Fractional Derivative and its Application to Fuzzy Fractional Partial DifferentialEquations

2021 ◽  
Author(s):  
Manizheh Ghaffari ◽  
Tofigh Allahviranloo ◽  
Saeid Abbasbandy ◽  
Mahdi Azhini
Keyword(s):  
Fractional Derivative ◽  
Analytical Method ◽  
Traveling Wave ◽  
Conformable Fractional Derivative ◽  
Fractional Wave Equation ◽  
Fractional Equations ◽  
Fuzzy Solution ◽  
Mathematical Equations ◽  
Traveling Wave Method ◽  
Generalized Hukuhara Differentiability

Abstract The main focus of this paper is to develop an efficient analytical method to obtain the traveling wave fuzzy solution for the fuzzy generalized Hukuhara conformable fractional equations by considering the type of generalized Hukuhara conformable fractional differentiability of the solution. To achieve this, the fuzzy conformable fractional derivative based on the generalized Hukuhara differentiability is defined, and several properties are brought on the topic, such as switching points and the fuzzy chain rule. After that, a new analytical method is applied to find the exact solutions for two famous mathematical equations: the fuzzy fractional Wave equation and the fuzzy fractional Diffusion equation. The present work is the first report in which the fuzzy traveling wave method is used to design an analytical method to solve these fuzzy problems. The final examples are asserted that our new method is applicable and efficient.

Explicit, periodic and dispersive soliton solutions to the conformable time-fractional Wu–Zhang system

2021 ◽  
pp. 2150417
Author(s):  
Kalim U. Tariq ◽  
Mostafa M. A. Khater ◽  
Muhammad Younis
Keyword(s):  
Fractional Derivative ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Conformable Fractional Derivative ◽  
Physical Behavior ◽  
Wave Solutions

In this paper, some new traveling wave solutions to the conformable time-fractional Wu–Zhang system are constructed with the help of the extended Fan sub-equation method. The conformable fractional derivative is employed to transform the fractional form of the system into ordinary differential system with an integer order. Some distinct types of figures are sketched to illustrate the physical behavior of the obtained solutions. The power and effective of the used method is shown and its ability for applying different forms of nonlinear evolution equations is also verified.

Bifurcations and Exact Solutions for a Class of MKdV Equations with the Conformable Fractional Derivative via Dynamical System Method

2020 ◽  
Vol 30 (01) ◽  
pp. 2050004 ◽  
Author(s):  
Jianli Liang ◽  
Longkun Tang ◽  
Yonghui Xia ◽  
Yi Zhang
Keyword(s):  
Fractional Derivative ◽  
Exact Solutions ◽  
Fractional Order ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Leibniz Rule ◽  
Wave Transformation ◽  
Conformable Fractional Derivative ◽  
Simplest Equation Method

In 2014, Khalil et al. [2014] proposed the conformable fractional derivative, which obeys chain rule and the Leibniz rule. In this paper, motivated by the monograph of Jibin Li [Li, 2013], we study the exact traveling wave solutions for a class of third-order MKdV equations with the conformable fractional derivative. Our approach is based on the bifurcation theory of planar dynamical systems, which is much different from the simplest equation method proposed in [Chen & Jiang, 2018]. By employing the traveling wave transformation [Formula: see text] [Formula: see text], we reduce the PDE to an ODE which depends on the fractional order [Formula: see text], then the analysis depends on the order [Formula: see text]. Moreover, as [Formula: see text], the exact solutions are consistent with the integer PDE. However, in all the existing papers, the reduced ODE is independent of the fractional order [Formula: see text]. It is believed that this method can be applicable to solve the other nonlinear differential equations with the conformable fractional derivative.

scholarly journals Analytical solutions for conformable fractional Bratu-type equations

2018 ◽  
Vol 7 (1) ◽  
pp. 15 ◽  
Author(s):  
Mousa Ilie ◽  
Jafar Biazar ◽  
Zainab Ayati
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Analytical Method ◽  
Conformable Fractional Derivative ◽  
Fractional Differential

Solving fractional differential equations have a prominent function in different science such as physics and engineering. Therefore, are different definitions of the fractional derivative presented in recent years. The aim of the current paper is to solve the fractional differential equation by a semi-analytical method based on conformable fractional derivative. Fractional Bratu-type equations have been solved by the method and to show its capabilities. The obtained results have been compared with the exact solution.

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

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
R. I. Nuruddeen ◽  
Khalid K. Ali ◽  
Lawal Muhammad ◽  
M. S. Osman ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Mathematical Physics ◽  
Order Derivative ◽  
Conformable Fractional Derivative ◽  
Fractional Order Derivative ◽  
De Vries ◽  
Fifth Order ◽  
2D And 3D

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.

scholarly journals Series method to solve conformable fractional ric-cati differential equations

2017 ◽  
Vol 6 (1) ◽  
pp. 30
Author(s):  
Mohammed Al Masalmeh
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Control ◽  
Series Solution ◽  
Stochastic Games ◽  
Variable Coefficients ◽  
Conformable Fractional Derivative ◽  
Series Method ◽  
Previous Definition ◽  
Hyperbolic Boundary

This paper investigates and states some properties of conformable fractional derivative, Further Study and applies the series solution for a case of conformable fractional Riccati deferential equation with variable coefficients “which is arising in stochastic games” or “hyperbolic boundary control." Recently, Prof. Roshdi Khalil introduced a new and interesting definition for the C F D, which is simpler than the previous definition in Caputo and Riemann-Liouville. It leads to many extensions of the classical theorems in calculus.

scholarly journals FTS and FTB of Conformable Fractional Order Linear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Abdellatif Ben Makhlouf ◽  
Omar Naifar ◽  
Mohamed Ali Hammami ◽  
Bao-wei Wu
Keyword(s):  
Fractional Derivative ◽  
Linear Systems ◽  
Fractional Order ◽  
Finite Time ◽  
Conformable Fractional Derivative ◽  
Time Stability ◽  
Order Linear ◽  
Finite Time Stability ◽  
Finite Time Boundedness

In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.

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