Computational Approaches for Analyzing Fractional Impulsive Systems in Differential Equations

Document Type : Research Paper

Authors

1 Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

2 Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.

Abstract

This research introduces an algorithmically efficient framework for analyzing the fractional impulsive system, which can be seen as specific instances of the broader fractional Lorenz impulsive system. Notably, these systems find pertinent applications within the financial domain. To this end, the utilization of cubic splines is embraced to effectively approximate the fractional integral within the context of the system. The outcomes derived from this method are subsequently compared with those yielded by alternative techniques documented in existing literature, all pertaining to the integration of functions.
Furthermore, the proposed methodology is not only applied to the resolution of fractional impulsive system, but also extended to encompass scenarios involving the fractional Lorenz system with impulsive characteristics. The discernible effects stemming from the selection of disparate impulse patterns are meticulously demonstrated. In synthesis, this paper endeavors to present a pragmatic and proficient resolution to the intricate challenges posed by impulsive systems.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 08 July 2024

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History

  • Receive Date: 27 April 2024
  • Revise Date: 09 June 2024
  • Accept Date: 25 June 2024

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