Current Developments in Mathematical Sciences

Current Developments in Mathematical Sciences

Volume: 1

Frontiers in Fractional Calculus

This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics ...
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Solving Fractional Diffusion Equation by Wavelet Methods

Pp. 1-32 (32)

Zhijiang Zhang and Weihua Deng


The wavelet numerical methods for solving the classic differential equations have been well developed, but their application in solving fractional differential equations is still in its infancy. In this chapter we tentatively investigate the advantages of the spline wavelet basis functions in solving the fractional PDEs. Our contributions are as follows: 1. the techniques of efficiently generating stiffness matrix with computational cost


Fractional PDEs, Wavelet preconditioning, Wavelet adaptivity, FFT and FWT.


School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China.