Fractional calculus is a branch of mathematics that deals with the differentiation and integration of any arbitrary order. Fractional differential equations have been widely applied to the analysis of complex systems such as material mechanics, anomalous diffusion, wave propagation and turbulence analysis, and researches on this field have attracted more and more attention in recent years. The variable order fractional calculus is the extension of the constant order fractional calculus. Here, fractional order is expressed not as a constant but in the form of a function of time or space variables.
Variable order fractional derivatives have significant advantages over constant order fractional derivatives in analyzing and controlling various physical systems including a nonlinear viscoelasticity oscillator.
Since numerical schemes with high degree of accuracy for variable order fractional derivatives can improve the accuracy of calculations and reduce computational cost, developing these numerical schemes is of great practical importance.
O Chol Won, a researcher at the Faculty of Applied Mathematics, has presented an explicit finite difference method for a space-time Riesz-Caputo variable order fractional wave equation.
He has proved that the explicit finite difference scheme is stable under certain constraints and estimated global truncation error. The numerical example shows the efficiency of the proposed finite difference scheme.
For further details, you can refer to his paper “An Explicit Finite Difference Approximation for Space-Time Riesz–Caputo Variable Order Fractional Wave Equation Using Hermitian Interpolation” in “NUMERICAL ANALYSIS AND APPLICATIONS” (SCI).
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