Abstract
This research paper explores novel theorems related to fractional differential operators, including Grunwald-Letnikov, Riemann-Liouville, Caputo, and Weyl. Each operator is rigorously defined, and their mathematical properties are investigated. The paper presents a detailed analysis of the asymptotic behavior of solutions to fractional differential equations governed by these operators. The advantages and disadvantages of each operator in capturing non-local behaviors, power-law decay, and handling initial conditions are discussed. Special emphasis is given to the stability characteristics of solutions, shedding light on the suitability of these operators for different types of problems. Through a comparative study, we highlight the unique features and computational challenges associated with each fractional derivative. Theoretical results are complemented by numerical simulations, providing insights into the practical implications of choosing a particular fractional operator in real-world applications.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Research in Science and Technology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
