The Numerical Solution of Fractional Diffusion Equation by Using Local Polynomial Regression

H. Caglara, N. Caglarb, M. Ozerc aIstanbul Kultur University, Department of Mathematics-Computer, Istanbul, Turkey bIstanbul Kultur University, Faculty of Economic and Administrative Science, Istanbul, Turkey cIstanbul Kultur University, Department of Physics, Istanbul, Turkey

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In this paper, we apply the local polynomial regression for the solution of the one-dimensional fractional diffusion equation. The Caputo fractional derivative is used for the formulation. A numerical example is given to show the application of the present method. The effect of the fractional order (α) of the equation is illustrated by changing α from 1.01 to 1.99.

DOI: 10.12693/APhysPolA.125.551 PACS numbers: 02.60.-x, 02.60.Lj