Solving fractional integro-differential equations by Aboodh transform

Volume 32, Issue 3, pp 229--240 http://dx.doi.org/10.22436/jmcs.032.03.04

Publication Date: September 29, 2023 Submission Date: June 26, 2023 Revision Date: June 30, 2023 Accteptance Date: July 23, 2023

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Authors

P. Raghavendran - Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\(\&\)D Institute of Science and Technology, Chennai-600062, Tamil Nadu, India. Th. Gunasekar - Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\(\&\)D Institute of Science and Technology, Chennai-600062, Tamil Nadu, India. H. Balasundaram - Department of Mathematics, Rajalakshmi Institute of Technology, Chennai-600124, Tamil Nadu, India. Sh. S. Santra - Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India. D. Majumder - Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India. D. Baleanu - Department of Mathematics, Faculty of Arts and Sciences, Çankaya University, Ankara, 06790 Etimesgut, Turkey. - Instiute of Space Sciences, 077125 Magurele, Magurele-Bucharest, Romania. - Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, Republic of China.

Abstract

This study approaches some families of fractional integro-differential equations (FIDEs) using a simple fractional calculus method, which leads to several appealing consequences, including the classical Frobenius method, which is generalized. The method presented here is based mostly on certain general theorems on particular solutions of FIDEs using the Aboodh transform and binomial series extension coefficients. We additionally demonstrate techniques to solve FIDEs.

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Keywords

• Riemann-Liouville (RL)
• fractional integral
• fractional-order differential equation
• gamma function
• Mittag-Leffler function
• Wright function
• Aboodh transform of the fractional derivative

MSC

•  26A33
•  31A10
•  33C10
•  34A05
•  35K37

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