Involvement of three successive fractional derivatives in a system of pantograph equations and studying the existence solution and MLU stability

Abstract

Developing a model of fractional differential systems and studying the existence and stability of a solution is considebly one of the most important topics in the field of analysis. Therefore, this manuscript was dedicated to deriving a new type of fractional system that arises from the combination of three sequential fractional derivatives with fractional pantograph equations. Also, the fixed-point technique was used to evaluate the existence and uniqueness of solutions to the supposed hybrid model. Furthermore, stability results for the intended system in the sense of the Mittag-Leffler-Ulam have been investigated. Ultimately, an illustrative example has been highlighted in order to reinforce the theoretical results and suggest applications for this article.

Keywords

• gronwall’s inequalities
• fixed-point techniques
• fractional derivatives
• stability analysis
• evaluation metrics
• 47h10
• 26a33
• 34a08
• 34b15