Ulam-Hyers Stability of Non-instantaneous Impulsive Integro-differential Equation of Real-order with Caputo Derivative with Application to Circuits
Matap Shankar and Swaroop Nandan Bora
Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati 781039, India
Received on February 16, 2024, revised on April 30, 2024
Accepted on April 30, 2024
Communicated by Gaston M. N'Guérékata
| Abstract. In this work, we first discuss the existence of a mild solution of the Caputo fractional non-instantaneous impulsive integro-differential equation and then discuss its stability in the sense of Ulam-Hyers. We establish our main results by using the well-known Banach fixed point theorem. Two suitable examples are presented to authenticate the results. In addition, with the help of the obtained results, the bound for a non-instantaneous impulsive fractional-order RLC circuit current is estimated, and it is found that the bound primarily depends upon the bandwidth and the fractional order of the RLC system. Further, for a given bandwidth, we show how the fractional order of the system influences the behavior and magnitude of the current. | |
| Keywords: | Ulam-Hyers stability, Non-instantaneous impulsive fractional differential equation, Banach fixed point theorem, Fractional-order RLC circuits, Ulam-Hyers constant. |
| 2010 Mathematics Subject Classification: 26A33, 33E12, 34A08, 35R12, 47N70. | |