On the Uniqueness of the Bounded Solution for the Fractional Nonlinear Partial Integro-Differential Equation with Approximations

This paper studies the uniqueness of bounded solution to a new Cauchy problem fractional nonlinear partial integro-differential equation based on multivariate Mittag–Leffler function as well Banach’s contractive principle in complete space. Applying Babenko’s approach, we convert with variable coefficients an implicit integral equation, which is powerful method studying solutions. Furthermore, construct algorithms for finding analytic and approximate solutions using Adomian’s decomposition recurrence relation order convergence analysis. Finally, illustrative example presented demonstrate constructions numerical MATHEMATICA.