This paper is concerned with the numerical solution of the time fractional coupled Burgers' equation. The proposed hybrid solution is based on Chebyshev collection method for space variable, and the trapezoidal quadrature technique. Finally the error analysis is discussed and some test examples are presented to demonstrate the applicability and efficiency of the method. c 2017 all rights reserved.
In this study we propose a hybrid spectral exponential Chebyshev method (HSECM) for solving time-fractional coupled Burgers equations (TFCBEs). The method is based upon a spectral collection method, utilizing exponential Chebyshev functions in space and trapezoidal quadrature formula (TQF), and also a finite difference method (FDM) for time-fractional derivative. Some test examples are included to demonstrate the efficiency and validity of the proposed method.
In opposite to differentiation and integration of integer order, an important type of differentiation and integration is the so - called “ Fractional Calculus (FC) ” in which the differentiation and integration is of non-integer order. The idea of this work is to use a new transformation known as the Extension AL-Zughair Transform (EZT) for fractional calculus, so we reviewed some basic properties and definitions of (FC) such as differentiation and integration with Riemann-Liouvial operator. We reinforced this transformation for fractional differentiation and integration with some application examples at the end of the article for simplicity the Fractional Integrals and Fractional Derivatives
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