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All Journal International Journal of Robotics and Control Systems
Aljazzazi, Mazin
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Control & Systems Engineering Electrical & Electronics Engineering

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Study and Analysis of the Second Order Constant Coefficients and Cauchy-Euler Equations via Modified Conformable Operator Bouchenak, Ahmad; Batiha, Iqbal M.; Hatamleh, Raed; Aljazzazi, Mazin; Jebril, Iqbal H.; Al-Horani, Mohammed
International Journal of Robotics and Control Systems Vol 5, No 2 (2025)
Publisher : Association for Scientific Computing Electronics and Engineering (ASCEE)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31763/ijrcs.v5i2.1577

Abstract

In this paper, we are concerned with a new modified conformable operator. Such an operator makes the study very easy in fractional calculus because it satisfies the most properties as the usual derivative and gives exact solutions. Furthermore, we will analyze and study the second-order fractional linear homogeneous differential equation with constant coefficients, which has two reasons for the importance of these types of differential equations. First of all, they often arise in applications. Second, it is relatively easy to find fundamental sets of solutions to these equations. In addition, we will also analyze the related fractional Cauchy–Euler type equation, which is used in various fields, physics, engineering, etc. Finally, as an application, we will illustrate the method on some numerical examples of the mentioned type of fractional differential equations.
Analytical Investigation of the Existence and Ulam Stability of Integro-Differential Equations with Conformable Derivatives Under Non-Local Conditions Fakhreddine, Seddiki; Hazaymeh, Ayman A; Aljazzazi, Mazin; Qaralleh, Reham; Bataihah, Anwar; Batiha, Iqbal M.; Hajaj, Rasha Ibrahim
International Journal of Robotics and Control Systems Vol 5, No 2 (2025)
Publisher : Association for Scientific Computing Electronics and Engineering (ASCEE)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31763/ijrcs.v5i2.1828

Abstract

This study examines an integro-differential equation involving fractional conformable derivatives and non-local conditions. It proves the existence and uniqueness of mild solutions by applying the Banach fixed-point theorem. Furthermore, it demonstrates a notable result about the existence of at least one solution, backed by conditions based on the Krasnoselskii fixed-point theorem. The investigation also explores the Ulam stability of integro-differential equations. To highlight the practical relevance and robustness of the findings, an illustrative example is provided.
Co-Authors Al-Horani, Mohammed Bataihah, Anwar Batiha, Iqbal M. Bouchenak, Ahmad Fakhreddine, Seddiki Hajaj, Rasha Ibrahim Hatamleh, Raed Hazaymeh, Ayman A Jebril, Iqbal H. Qaralleh, Reham