TY - JOUR
T1 - An Inverse Operator Approach to a Fractional Nonlinear Integro-Differential Equation
AU - Li , Chenkuan
AU - Liao , Wenyuan
AU - Saadati , Reza
JO - Analysis in Theory and Applications
VL - 2
SP - 172
EP - 196
PY - 2025
DA - 2025/07
SN - 41
DO - http://doi.org/10.4208/ata.OA-2024-0043
UR - https://global-sci.org/intro/article_detail/ata/24281.html
KW - Fractional nonlinear integro-differential equation, uniqueness and existence, fixed point theory, multivariate Mittag-Leffler function, inverse operator.
AB - <p style="text-align: justify;">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 to
convert the equation into an equivalent implicit integral equation based on a bounded
inverse operator which is an infinite series and uniformly convergent. Furthermore,
we compute approximate values of a few multivariate Mittag-Leffler functions by our
Python codes in illustrative examples demonstrating the use of key theorems derived.
These investigations have a wide range of applications as existence, uniqueness and
stability often appear in various pure and applied research areas.</p>