Local Fractional Operator for a One-Dimensional Coupled Burger Equation of Non-Integer Time Order Parameter

In this study, approximate solutions of a system of time-fractional coupled Burger equations were obtained by means of a local fractional operator (LFO) in the sense of the Caputo derivative. The LFO technique was built on the basis of the standard differential transform method (DTM). Illustrative examples used in demonstrating the effectiveness and robustness of the proposed method show that the solution method is very efficient and reliable as "“ unlike the variational iteration method "“ it does not depend on any process of identifying Lagrange multipliers, even while still maintaining accuracy

Local Fractional Operator for a One-Dimensional Coupled Burger Equation of Non-Integer Time Order Parameter

In this study, approximate solutions of a system of time-fractional coupled Burger equations were obtained by means of a local fractional operator (LFO) in the sense of the Caputo derivative. The LFO technique was built on the basis of the standard differential transform method (DTM). Illustrative examples used in demonstrating the effectiveness and robustness of the proposed method show that the solution method is very efficient and reliable as – unlike the variational iteration method – it does not depend on any process of identifying Lagrange multipliers, even while still maintaining accuracy

FRDTM for numerical simulation of multi-dimensional, time-fractional model of Navier–Stokes equation

AbstractIn this paper, a new approximate solution of time-fractional order multi-dimensional Navier–Stokes equation is obtained by adopting a semi-analytical scheme: “Fractional Reduced Differential Transformation Method (FRDTM)”. Three test problems are carried out in order to validate and illustrate the efficiency of the method. The scheme is found to be very reliable, effective and efficient powerful technique to solve wide range of problems arising in engineering and sciences. The small size of computation contrary to the other schemes, is its strength

Analytical Solutions of a 1D Time-fractional Coupled Burger Equation via Fractional Complex Transform

In this paper, we obtain analytical solutions of a system of time-fractional coupled Burger equation of one-dimensional form via the application of Fractional Complex Transform (FCT) coupled with a modified differential transform method (MDTM) in comparison with Adomian Decomposition Method ADM). The associated fractional derivatives are defined in terms of Jumarie’s sense. Illustrative cases are considered in clarifying the effectiveness of the proposed technique. The method requires minimal knowledge of fractional calculus. Neither linearization nor discretization is involved. The results are also presented graphically for proper illustration and efficiency is ascertained. Hence, the recommendation of the method for linear and nonlinear space-fractional models

SOLVING BURGER’S AND COUPLED BURGER’S EQUATIONS WITH CAPUTO-FABRIZIO FRACTIONAL OPERATOR

In this paper, we apply Daftardar-Jafari method (DJM) to obtain approximate solutions of the nonlinear Burgers (NBE) and coupled nonlinear Burger’s equations (CNBEs) with Caputo-Fabrizio fractional operator (CFFO). The efficiency of the considered method is illustrated by some examples. Graphical results are utilized and discussed quantitatively to illustrate the solution. The results reveal that the suggested algorithm is very effective and simple and can be applied for other problems in sciences and engineering

Construction of (n+ 1) -dimensional dual-mode nonlinear equations: multiple shock wave solutions for (3 + 1) -dimensional dual-mode Gardner-type and KdV-type

The goal of this study is to offer an exclusive functional conversion to produce (n+ 1) -dimensional dual-mode nonlinear equations. This transformation has been implemented and new (3 + 1) -dimensional dual-mode Gradner-type and KdV-type have been established. Finally, the simplified bilinear method is used to tell the necessary conditions on these new models to have multiple singular-solitons. - 2019, The Author(s).This work is financially supported by UKM Grant: DIP-2017-011 and Ministry of Education Malaysia Grant FRGS/1/2017/STG06/UKM/01/1.Scopu

A New Coupled Fractional Reduced Differential Transform Method for the Numerical Solutions of (2+1)-Dimensional Time Fractional Coupled Burger Equations

A very new technique, coupled fractional reduced differential transform, has been implemented to obtain the numerical approximate solution of (2 + 1)-dimensional coupled time fractional burger equations. The fractional derivatives are described in the Caputo sense. By using the present method we can solve many linear and nonlinear coupled fractional differential equations. The obtained results are compared with the exact solutions. Numerical solutions are presented graphically to show the reliability and efficiency of the method

Review of Some Promising Fractional Physical Models

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods of the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of non-integer order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.Comment: 38 pages, LaTe