Bernoulli Wavelets Method for Solution of Fractional Differential Equations in a Large Interval

Authors
E Keshavarz
Y Ordokhani
10.29252/mmr.2.1.17
Abstract
In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van der Pol and Bagley-Torvik equations for the application of the method. Illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method.
Keywords
Wavelet
Fractional calculus
Differential equations
Block pulse function
Van der Pol equation
Bagley-Torvik equation
Caputo derivative
Operational matrix
Numerical solution
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