Analysis on Krasnoselskii’s fixed point theorem of fuzzy variable fractional differential equation for a novel coronavirus(COVID-19)model with singular operator

The fuzzy variable fractional differential equations(FVFDEs)play a very important role in mathematical modeling of COVID-19.The scientists are studying and developing several aspects of these COVID-19 models.The existence and uniqueness of the solution,stability analysis are the most common and important study aspects.There is no study in the literature to establish the existence,uniqueness,and UH stability for fuzzy variable fractional(FVF)order COVID-19 models.Due to high demand of this study,we investigate results for the existence,uniqueness,and UH stability for the considered COVID-19 model based on FVFDEs using a fixed point theory approach with the singular operator.Additionally,discuss the maximal/minimal solution for the FVFDE of the COVID-19 model.

Ulam-Hyers stability and analytical approach for m-dimensional Caputo space-time variable fractional order advection-dispersion equation

This article introduces the computational analytical approach to solve the m-dimensional space-time variable Caputo fractional order advection–dispersion equation with the Dirichlet boundary using the two-step Adomian decomposition method and obtain the exact solution in just one iteration.Moreover,with the help of fixed point theory,we study the existence and uniqueness conditions for the positive solution and prove some new results.Also,obtain the Ulam–Hyers stabilities for the proposed problem.Two gen-eralized examples are considered to show the method’s applicability and compared with other existing numerical methods.The present method performs exceptionally well in terms of efficiency and simplicity.Further,we solved both examples using the two most well-known numerical methods and compared them with the TSADM solution.