Abstract
A new method based on a hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear fractional differential equations. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of linear or nonlinear algebraic equations. This method can be considered as a nonuniform finite difference method. Some examples are given to verify and illustrate the efficiency and simplicity of the proposed method.
Highlights
The study of fractional calculus dates back to 17th century, starting by G
In view of (5), Chebyshev wavelets are an orthonormal set with respect to the weight function wn(x) because
The numerical results for β = 1 and different values of α plotted in Figure 6 show that as α tends to 2, the solution of fractional differential equation approaches to that of the integer-order differential equation
Summary
The study of fractional calculus dates back to 17th century, starting by G. An increasing number of numerical methods were being developed These methods include homotopy analysis method [7], homotopy perturbation method [8,9,10], variational iteration method [9,10,11,12,13], finite difference method [5, 14,15,16,17,18], Adomian decomposition method [19,20,21,22,23], fractional differential transform method [24, 25], predictorcorrector method [26], fractional linear multistep method [27], extrapolation method [28], integral transform [29], and generalized block pulse operational matrix method [30, 31].
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