Comparative Analysis of Fractional Derivative Operators: Stability, Asymptotic Behavior, and Computational Challenges
Rajkumari Pratima Devi
Department of Mathematics, Manipur International University, Imphal, India
Md. Indraman Khan
Department of Mathematics, PETTIGREW College, Ukhrul, Manipur University, Manipur
13-23
Vol: 14, Issue: 2, 2024
Receiving Date:
2024-03-01
Acceptance Date:
2024-04-09
Publication Date:
2024-04-09
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http://doi.org/10.37648/ijrst.v14i02.002
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.
Keywords:
Fractional calculus; Grunwald-Letnikov; Riemann-Liouville; Caputo; Weyl operators; Fractional differential equations; Asymptotic behavior
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