Methods of Fractional Differential Equations in Algebra and Calculus

Author(s)	Konthoujam Ibochouba Singh, Md. Indraman Khan, Prof. Irom Tomba Singh
Country	India
Abstract	This paper introduces a novel approach, the Inverse Fractional Shehu Transform Method, for solving both homogeneous and non-homogeneous linear fractional differential equations. The fractional derivatives are considered in the Riemann-Liouville and Caputo senses. By applying the Laplace transform and the convolution product to the Riemann-Liouville fractional of matrices, we obtain accurate solutions for systems of matrix fractional differential equations. The method’s effectiveness is demonstrated through examples, and its accuracy is verified by comparing the results with existing solutions in the literature. A numerical algorithm of fractional differential algebraic equations in terms of the theory of sliding mode control and the Grunwald-Letnikov is proposed assuming sliding mode surface.
Keywords	Inverse Fractional Shehu transform, Riemann-Liouville fractional derivative, Differential-Algebraic Equations, Sliding Mode Control, Laplace Transform
Published In	Volume 16, Issue 2, April-June 2025
Published On	2025-06-26

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