On the Solution of Burgers’ Equation with the New Fractional Derivative
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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.Abstract:
Abstract Firstly 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.read more
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New exact solutions of Burgers’ type equations with conformable derivative
TL;DR: In this paper, the exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative of the Burgers-Korteweg-de Vries equation.
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Soliton solutions of the conformable fractional Zakharov–Kuznetsov equation with dual-power law nonlinearity
TL;DR: In this paper, the Riccati sub equation method is employed to solve fractional Zakharov-Kuznetsov equation with dual-power law nonlinearity in the sense of the conformable derivative.
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Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative
TL;DR: In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method (CADM).
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Exact solutions to the space–time fractional Schrödinger–Hirota equation and the space–time modified KDV–Zakharov–Kuznetsov equation
TL;DR: In this paper, the first integral method and functional variable method are used to establish exact traveling wave solutions of the space-time fractional Schrodinger-Hirota equation and the space time fractional modified KDV-Zakharov-Kuznetsov equation in the sense of conformable fractional derivative.
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Traveling wave solutions for (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity
TL;DR: In this article, the (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity was considered and solved by means of a unified method.
References
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An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
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Beyond Perturbation: Introduction to the Homotopy Analysis Method
Shijun Liao,SA Sherif +1 more
TL;DR: In this paper, a simple bifurcation of a nonlinear problem multiple solutions of a Nonlinear Problem Nonlinear Eigenvalue Problem Thomas-Fermi Atom Model Volterra's Population Model Free Oscillation Systems with Odd Nonlinearity Free oscillations with Quadratic nonlinearity Limit Cycle in a Multidimensional System Blasius' viscous flow Boundary-layer Flow Boundarylayer Flow with Exponential Property Boundary Layer Flow with Algebraic Property Von Karman Swirling Flow Nonlinear Progressive Waves in Deep Water BIBLIOGR
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On a quasi-linear parabolic equation occurring in aerodynamics
TL;DR: In this paper, the Navier-Stokes equations for one-dimensional non-stationary flow of a compressible viscous fluid are compared to the shock wave theory of a model of turbulence.