Semi-Analytical Analysis of Advection Dispersion and Parabolic Time-Fractional Fuzzy Models by Using the Fractional Variational Iterative Method

Uncertainty in parameters is handled through fuzzy differential models, while their solution can elaborate on their stability. Iterative methods are powerful tools to express the approximate solution up to a finite order of iteration; therefore, here we are analyzing two renowned time-fractional fuzzy differential equation models, advection dispersion and parabolic, through the fractional variational iterative method (FVIM). In the meanwhile Riemann-Liouville fractional integral is used to evaluate the time-fractional order derivative. Exact solution of advection dispersion equation in the form of Mittag-Leffler function for integer order is obtained, and other approximate solutions for non-integer derivatives are also discussed, while the exact solution of parabolic equation is also obtained in the form of Mittag-Leffler function. All numerical results for both time-fractional fuzzy partial differential equation models are discussed and compared with existing solutions. Moreover, numerical solutions of non-integer derivatives are also obtained.