شماره ركورد كنفرانس :
3735
عنوان مقاله :
Second-order approximations for variable order fractional derivatives: Algorithms and applications
پديدآورندگان :
Gholamnia Sahar sahargholami7010@yahoo.com Shahid Chamran University of Ahvaz , Jalalvand Mehdi m.jalalvand@scu.ac.ir Shahid Chamran University of Ahvaz , nabati Mohammad nabati@put.ac.ir Petroleum university of technology Abadan
كليدواژه :
Variable , order fractional operators , High , order , Anomalous diffusion , Wave , propagation , Burgers equation
عنوان كنفرانس :
اولين كنفرانس منطقه اي علوم رياضي و كاربردها
چكيده فارسي :
Fractional calculus allows variable-order of fractional operators, which can be ex
ploited in diverse physical and biological applications where rates of change of the
quantity of interest may depend on space and/or time. In this paper, we derive two
secondorder approximation formulas for the variable-order fractional time derivatives
involved in anomalous diffusion and wave propagation. We then present numerical
tests that verify the theoretical estimates of convergence rate and also simulations of
anomalous subdiffusion and super-diffusion that demonstrate new localized diffusion
rates that depend on the curvature of the variable-order function. Finally, we perform
simulations of wave propagation in a truncated domain to demonstrate how erroneous
wave reflections at the boundaries can be eliminated by super-diffusion, and also simu
lations of the Burgers equation that serve as a testbed for studying the loss and recovery
of monotonicity using again variable rate diffusion as a function of space and/or time.