卡鲁塔变换及其在卡普托微分方程中的应用

Nikita Kumawat, Akanksha Shukla, M. Mishra, Rahul Sharma, Ravi Shanker Dubey
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引用次数: 0

摘要

本文旨在利用一种积分变换,特别是 Khalouta 变换(各种积分变换的抽象),来处理使用黎曼-刘维尔和卡普托分数导数的分数微分方程。我们讨论了这种积分变换的一些结果和存在性。此外,我们还讨论了 Shehu 变换和 Khalouta 变换之间的对偶性。我们提供了一些数值示例,以证实所提出的分数微分方程求解方法的适用性和正确性。
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Khalouta transform and applications to Caputo-fractional differential equations
The paper aims to utilize an integral transform, specifically the Khalouta transform, an abstraction of various integral transforms, to address fractional differential equations using both Riemann-Liouville and Caputo fractional derivative. We discuss some results and the existence of this integral transform. In addition, we also discuss the duality between Shehu transform and Khalouta transform. The numerical examples are provided to confirm the applicability and correctness of the proposed method for solving fractional differential equations.Primary 92B05, 92C60; Secondary 26A33.
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