An Inverse Operator Approach to a Fractional Nonlinear Integro-Differential Equation (Analysis in Theory and Applications, 2025)
This paper studies the existence, uniqueness and stability for a new fractional nonlinear integro-differential equation with an integral boundary condition using several well-known fixed point theorems in a Banach space. The method used is toconvert the equation into an equivalent implicit integral equation based on a boundedinverse operator which is an infinite series and uniformly convergent. Furthermore,we compute approximate values of a few multivariate Mittag-Leffler functions by ourPython codes in illustrative examples demonstrating the use of key theorems derived.These investigations have a wide range of applications as existence, uniqueness andstability often appear in various pure and applied research areas.
Keywords: Fractional nonlinear integro-differential equation; uniqueness and existence; fixed point theory; multivariate Mittag-Leffler function; inverse operator.