Existence and uniqueness results of the AB-Caputo type derivative in impulsive fractional differential equations

Volume 39, Issue 4, pp 407--417 https://dx.doi.org/10.22436/jmcs.039.04.01

Publication Date: April 16, 2025 Submission Date: August 25, 2024 Revision Date: January 14, 2025 Accteptance Date: February 28, 2025

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Authors

K. Venkatachalam - Department of Mathematics, Nandha Engineering College (Autonomous), Erode - 638 052, Tamil Nadu, India. B. Batiha - Mathematics Department, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan. B. Almarri - General studies department, Jubail Industrial College, 8244 Rd Number 6, Al Huwaylat, Al Jubail 35718, Saudi Arabia. M. S. Kumar - Department of Mathematics, Paavai Engineering College (Autonomous), Namakkal - 637 018, Tamil Nadu, India. O. Bazighifan - Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout, Yemen. - Jadara Research Center, Jadara University, Irbid 21110, Jordan.

Abstract

In this work, we study the fractional differential equations solutions of Atangana-Baleanu-Caputo, which are subject to integral and impulsive boundary conditions. In addition, the Banach Contraction Mapping Principle and the Krasnoselskii fixed point theorems are employed for showing the existence and uniqueness of the theorems. An illustration is provided to support the outcomes of the results.

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Keywords

• AB-Caputo fractional
• integro-differential equations
• fixed point technique
• existence
• uniqueness

MSC

•  26A33
•  34A09
•  34A12
•  47H10

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