New approximations of space-time fractional Fokker-Planck equations

The present study focuses on the two new hybrid methods: variational iteration J-transform technique (J-VIT) and J-transform method with optimal homotopy analysis (OHAJTM) for analytical assessment of space-time fractional Fokker-Planck equations (STF-FPE), appearing in many realistic physical situations, e.g., in ultra-slow kinetics, Brownian motion of particles, anomalous diffusion, polymerases of Ribonucleic acid, deoxyribonucleic acid, continuous random movement, and formation of wave patterns. OHAJTM is developed via optimal homotopy analysis after implementing the properties of J-transform while (J-VIT) is produced by implementing properties of the J-transform and the theory of variational iteration. Banach approach is utilized to analyze the convergence of these methods. In addition, it is demonstrated that J-VIT is T-stable. Computed new approximations are reported as a closed form expression of the Mittag-Leffler function, and in addition, the effectiveness/validity of the proposed new approximations is demonstrated via three test problems of STF-FPE by computing the error norms: L2 and absolute errors. The numerical assessment demonstrates that the developed techniques perform better for STF-FPE and for a given iteration, and OHAJTM produces new approximations with better accuracy as compared to J-VIT as well as the techniques developed recently.