Mathematics

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https://hdl.handle.net/20.500.14540/131

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Browsing Mathematics by Advisor "Dr.Jeevan Kafle"

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    Numerical approaches for solving special functions in fractional calculus
    (Institute of Science & Technology, 2024-05) Pariyar, Shankar; Dr.Jeevan Kafle
    The study uses systemic diagrams to compare fractional equations at  values 0 <  < 1 with non-fractional equations at  = 1. Under Caputo Fabrizio's fractional differential equation, it looks at the identity, sine, and cosine functions. While avoiding non-zero fractional derivatives of constant functions, the Grunwald-Letinikov (G-L) numerical solution assures precision. Ensuring numerical results from fractional and traditional calculus remain comparable is the goal of this research. It is necessary to use non-linear operators because deviations arise when fractional orders diverge. Ideas such as curve smoothness and value fluctuations are made clear by illustrative examples. Additionally, utilizing MLF at different values of , , and  within the range 0 <  < 1, the study examines the numerical solution of one, two, and three parameters. It is shown how Magnus Gosta (M.G.) Mittag-Leffler's computations are used in scientific and practical fields. In order to familiarize with the latest research trends and MLF consequences, this study provides a thorough overview of the several types of Mittag-Leffler functions (MLF) that can be found in the literature. This research significantly enhances the knowledge of fractional derivatives and the integration of transcendental forms of functions. Using the Lagrange interpolation approach, we will demonstrate some numerical strategies, including the L1 scheme for 0 <  < 1, the L2 scheme for 1<  < 2, and the L1 method for the Caputo Fabrizio derivative.