Abstract
This chapter is concerned with fractional dynamic systems which occur in many engineering and scientific research fields. These include a variety of multiterm time/time-space fractional dynamic systems. The chapter presents the analytical solution for the multiterm time-fractional model; the fractional predictor-corrector method for the multiterm time-space fractional model, the fractional alternating-direction implicit method for the multiterm time-fractional Bloch–Torrey model, and the finite difference method for the multiterm time-fractional viscoelastic non-Newtonian fluid model. We rigorously analyze the stability and convergence of each numerical method. We also provide some applications of the theory and developed numerical schemes.
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