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Volume 41, Issue 2
An Inverse Operator Approach to a Fractional Nonlinear Integro-Differential Equation

Chenkuan Li, Wenyuan Liao & Reza Saadati

Anal. Theory Appl., 41 (2025), pp. 172-196.

Published online: 2025-07

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  • Abstract

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.

  • AMS Subject Headings

34B15, 34A12, 34K20, 26A33

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-41-172, author = {Li , ChenkuanLiao , Wenyuan and Saadati , Reza}, title = {An Inverse Operator Approach to a Fractional Nonlinear Integro-Differential Equation}, journal = {Analysis in Theory and Applications}, year = {2025}, volume = {41}, number = {2}, pages = {172--196}, abstract = {

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} }
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 -

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.

Li , ChenkuanLiao , Wenyuan and Saadati , Reza. (2025). An Inverse Operator Approach to a Fractional Nonlinear Integro-Differential Equation. Analysis in Theory and Applications. 41 (2). 172-196. doi:10.4208/ata.OA-2024-0043
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