Khalouta transform and applications to Caputo-fractional differential equations - Kumawat, Nikita; Shukla, Akanksha; Mishra, Manvendra Narayan; Sharma, Rahul; Dubey, Ravi Shanker (Frontiers in Applied Mathematics and Statistics, 2024)
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.