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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.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2024-0043}, url = {http://global-sci.org/intro/article_detail/ata/24281.html} }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.