Stieltjes integral boundary value problem involving a nonlinear multi-term Caputo-type sequential fractional integro-differential equation

• Published in: AIMS mathematics Vol. 8; no. 12; pp. 28413 - 28434
• Main Authors: Zhang, Jiqiang, Haq, Siraj Ul, Zada, Akbar, Popa, Ioan-Lucian
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2023
• Subjects: caputo derivative; existence; fixed point; hyers-ulam stability; mild solution; stieltjes boundary conditions
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.20231454

In this article, we analyze the existence and uniqueness of mild solution to the Stieltjes integral boundary value problem involving a nonlinear multi-term, Caputo-type sequential fractional integro-differential equation. Krasnoselskii's fixed-point theorem and the Banach contraction principle are utilized to obtain the existence and uniqueness of the mild solution of the aforementioned problem. Furthermore, the Hyers-Ulam stability is obtained with the help of established methods. Our proposed model contains both the integer order and fractional order derivatives. As a result, the exponential function appears in the solution of the model, which is a fundamental and naturally important function for integer order differential equations and its many properties. Finally, two examples are provided to illustrate the key findings.