Khalouta transform and applications to Caputo-fractional differential equations
Nikita Kumawat, Akanksha Shukla, Manvendra Narayan Mishra, Rahul Sharma, Ravi Shanker Dubey
Abstract
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. 2010 Mathematics Classification Primary 92B05, 92C60; Secondary 26A33.
Topics & Concepts
Fractional calculusMathematicsApplied mathematicsDifferential equationMathematical analysisFractional Differential Equations SolutionsNumerical methods in engineeringIterative Methods for Nonlinear Equations