Khalouta transform and applications to Caputo-fractional differential equations

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...

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Bibliographic Details
Published in:Frontiers in applied mathematics and statistics Vol. 10
Main Authors: Kumawat, Nikita, Shukla, Akanksha, Mishra, Manvendra Narayan, Sharma, Rahul, Dubey, Ravi Shanker
Format: Journal Article
Language:English
Published: Frontiers Media S.A 06-02-2024
Subjects:
Caputo fractional derivative
fractional differential equation
Khalouta transfom
Mittag-Leffler function
Riemann fractional derivative
Online Access:Get full text
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Summary: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.
ISSN:2297-4687
2297-4687
DOI:10.3389/fams.2024.1351526