scholarly journals On the Solution of Burgers’ Equation with the New Fractional Derivative

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Ali Kurt ◽  
Yücel Çenesiz ◽  
Orkun Tasbozan
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Fractional Derivative ◽  
Burgers Equation ◽  
Approximate Analytical Solution ◽  
Initial Conditions ◽  
Conformable Fractional Derivative ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Homotopy Analysis

AbstractFirstly in this article, the exact solution of a time fractional Burgers’ equation, where the derivative is conformable fractional derivative, with dirichlet and initial conditions is found byHopf-Cole transform. Thereafter the approximate analytical solution of the time conformable fractional Burger’s equation is determined by using a Homotopy Analysis Method(HAM). This solution involves an auxiliary parameter ~ which we also determine. The numerical solution of Burgers’ equation with the analytical solution obtained by using the Hopf-Cole transform is compared.

scholarly journals Approximate Analytical Solutions to Conformable Modified Burgers Equation Using Homotopy Analysis Method

2019 ◽  
Vol 33 (1) ◽  
pp. 159-167 ◽  
Author(s):  
Ali Kurt ◽  
Orkun Tasbozan
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Homotopy Analysis Method ◽  
Burgers Equation ◽  
Approximate Analytical Solution ◽  
Analysis Method ◽  
Conformable Derivative ◽  
Modified Burgers Equation ◽  
Approximate Analytical Solutions ◽  
Homotopy Analysis

AbstractIn this paper the authors aspire to obtain the approximate analytical solution of Modified Burgers Equation with newly defined conformable derivative by employing homotopy analysis method (HAM).

scholarly journals Homotopy Analysis Method for Conformable Burgers-Korteweg-de Vries Equation

2016 ◽  
Vol 17 ◽  
pp. 17-23 ◽  
Author(s):  
Ali Kurt ◽  
Orkun Tasbozan ◽  
Yücel Cenesiz
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Homotopy Analysis Method ◽  
Vries Equation ◽  
Approximate Analytical Solution ◽  
Analysis Method ◽  
Conformable Derivative ◽  
De Vries ◽  
Homotopy Analysis

The main goal of this paper is nding the approximate analytical solution of Burgers-Korteweg-de Vries with newly de ned conformable derivative by using homotopy analysis method (HAM). Then the approximate analytical solution is compared with the exact solution and comparative tables are given.

A New Semi-Analytical Solution of the Telegraph Equation with Integral Condition

2011 ◽  
Vol 66 (12) ◽  
pp. 760-768 ◽  
Author(s):  
S. Abbasbandy ◽  
H. Roohani Ghehsarehb
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Iterative Algorithm ◽  
Homotopy Analysis Method ◽  
Integral Condition ◽  
Telegraph Equation ◽  
Current Work ◽  
Analysis Method ◽  
Numerical Examples ◽  
Homotopy Analysis

In the current work, the telegraph equation in its general form and with an integral condition is investigated. Also the well-known homotopy analysis method (HAM) is applied and an interesting iterative algorithm is proposed for solving the problem in general form. Some numerical examples are given and compared with the exact solution to show the effectiveness of the proposed method.

scholarly journals LHAM Approach to Fractional Order Rosenau-Hyman and Burgers' Equations

2020 ◽  
pp. 1-14
Author(s):  
S. O. Ajibola ◽  
A. S. Oke ◽  
W. N. Mutuku
Keyword(s):  
Exact Solution ◽  
Fractional Order ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Convergent Series ◽  
Analytic Solutions ◽  
Fractional Dimension ◽  
Analysis Method ◽  
Burgers Equations ◽  
Homotopy Analysis

Fractional calculus has been found to be a great asset in finding fractional dimension in chaos theory, in viscoelasticity diffusion, in random optimal search etc. Various techniques have been proposed to solve differential equations of fractional order. In this paper, the Laplace-Homotopy Analysis Method (LHAM) is applied to obtain approximate analytic solutions of the nonlinear Rosenau-Hyman Korteweg-de Vries (KdV), K(2, 2), and Burgers' equations of fractional order with initial conditions. The solutions of these equations are calculated in the form of convergent series. The solutions obtained converge to the exact solution when α = 1, showing the reliability of LHAM.

scholarly journals On the New Solutions of the Conformable Time Fractional Generalized Hirota-Satsuma Coupled KdV System

2017 ◽  
Vol 55 (1) ◽  
pp. 37-50 ◽  
Author(s):  
Yucel Çenesiz ◽  
Ali Kurt ◽  
Orkun Tasbozan
Keyword(s):  
Fractional Derivative ◽  
Approximate Solutions ◽  
Solution Procedure ◽  
Nonlinear Pdes ◽  
Mathematical Tool ◽  
Conformable Fractional Derivative ◽  
Analysis Method ◽  
Tanh Method ◽  
Homotopy Analysis ◽  
Powerful Mathematical Tool

AbstractIn this paper, generalized Hirota Satsuma coupled KdV system is solved with tanh method and q-Homotopy analysis method. New fractional derivative definition called “conformable fractional derivative” used in the solution procedure. Tanh method with conformable derivative firstly introduced in the literature. By the graphics of analytical and approximate solutions, it is shown that, both methods provide an effective and powerful mathematical tool for solving nonlinear PDEs containing conformable fractional derivative.

scholarly journals SOME PROPERTIES OF FRACTIONAL BURGERS EQUATION

2002 ◽  
Vol 7 (1) ◽  
pp. 151-158 ◽  
Author(s):  
P. Miškinis
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Conservation Laws ◽  
Traveling Wave ◽  
Wave Solution ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Traveling Wave Solution ◽  
One Dimensional ◽  
Liouville Fractional Derivative

The fractional generalization of a one‐dimensional Burgers equationwith initial conditions ɸ(x, 0) = ɸ0(x); ɸt(x,0) = ψ0 (x), where ɸ = ɸ(x,t) ∈ C2(Ω): ɸt = δɸ/δt; aDx p is the Riemann‐Liouville fractional derivative of the order p; Ω = (x,t) : x ∈ E 1, t > 0; and the explicit form of a particular analytical solution are suggested. Existing of traveling wave solution and conservation laws are considered. The relation with Burgers equation of integer order and properties of fractional generalization of the Hopf‐Cole transformation are discussed.

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