Abstract
This chapter is devoted to the numerical solution of partial differential equations with fractional derivatives. A linear B-spline approximates the fractional derivatives along with an upwind finite difference method and the Du Fort–Frankel algorithm for the temporal and spatial discretizations. The proposed techniques include an explicit Adams–Bashforth method to improve their numerical stability and accuracy. Several numerical problems, such as the fractional Kolmogorov–Petrovskii–Piskunov, Newell–Whitehead–Segel, and FitzHugh–Nagumo equations, are presented to illustrate the efficiency and reliability of the algorithms.
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