J. Math. Computer Sci., 39 (2025), 407–417 Online: ISSN 2008-949X Journal Homepage: www.isr-publications.com/jmcs Existence and uniqueness results of the AB-Caputo type derivative in impulsive fractional differential equations Kuppusamy Venkatachalam a , Belal Batiha b , Barakah Almarri c,∗ , Marappan Sathish Kumar d , Omar Bazighifan e,f,∗ a Department of Mathematics, Nandha Engineering College (Autonomous), Erode - 638 052, Tamil Nadu, India. b Mathematics Department, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan. c General studies department, Jubail Industrial College, 8244 Rd Number 6, Al Huwaylat, Al Jubail 35718, Saudi Arabia. d Department of Mathematics, Paavai Engineering College (Autonomous), Namakkal - 637 018, Tamil Nadu, India. e Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout, Yemen. f 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. Keywords: AB-Caputo fractional, integro-differential equations, fixed point technique, fractional calculus, AB-Caputo fractional, existence, uniqueness. 2020 MSC: 26A33, 34A09, 34A12, 47H10. ©2025 All rights reserved. 1. Introduction Fractional calculus is the examination of differential and integral operators with real or complex or- ders. Fractional calculus has experienced a significant increase in importance and utilisation over the past forty years due to its wide range of applications in various scientific fields and technology. The concept of fractional operators was developed and mathematically formalised in the past few years. The various characteristics of fractional operators have sparked significant interest in the field of fractional calculus in recent times, along with a diverse array of practical uses, particularly in simulating physical phenomena. Fractional derivatives (FDr’s) and integrals have been extensively utilized over the past few decades to en- hance the accuracy of mathematical models. The growing significance of fractional calculus is attributed ∗ Corresponding authors Email addresses: venkatachalam.k@nandhaengg.org (Kuppusamy Venkatachalam), b.bateha@jadara.edu.jo (Belal Batiha), marribj@rcjy.edu.sa (Barakah Almarri), msksjv@gmail.com (Marappan Sathish Kumar), o.bazighifan@gmail.com (Omar Bazighifan) doi: 10.22436/jmcs.039.04.01 Received: 2024-08-25 Revised: 2025-01-14 Accepted: 2025-02-28