A STUDY OF RICCATI’S FRACTIONAL DIFFERENTIAL EQUATION USING KAMAL INTEGRAL TRANSFORM BY ADOMIAN DECOMPOSITION APPROACH
By
Heena Siddiqui1 , Devilal Kumawat2* and Kuldeep Singh Gahlot3
1Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur, Rajasthan, India - 342001
2Department of Education, Jain Vishva Bharati Institute (Deemed to be University), Ladnun, Rajasthan, INDIA - 341306
3Department of Mathematics, Government College, Sadri, Pali, Rajasthan, India - 306702
Email: *devilalkumawat225@gmail.com, siddiquiheena1991@gmail.com, drksgehlot@rediffmail.com
(Received: July 25, 2024; In format September 18, 2024; Revised: May 18, 2025; Accepted: June 11, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55120
Abstract
The main purpose of this study is to solve Riccati’s fractional differential equations (RFDE) using the Kamal integral transform by Adomian decomposition approach. In addition, the Adomian decomposition approach and the combined Kamal integral transformation method were used to study the solution of Riccati’s fractional differential equation. The most important conclusions of our research demonstrate the high accuracy of the Adomian decomposition approach and the Kamal integral transformation while solving Riccati’s fractional differential equations. In order to solve the fractional differential equations of Riccati’s, the current results are novel and unique. The outcomes of this study validate that a few examples have been resolved to demonstrate the effectiveness of the suggested approach.
This study introduces a novel method for solving Riccati fractional differential equations (RFDEs) by combining the Kamal integral transform with the Adomian decomposition method. The integrated approach effectively addresses the nonlinear nature of RFDEs, offering an accurate and systematic solution technique. Comparative analysis demonstrates the high precision and efficiency of the proposed method. The results are both innovative and distinct, contributing new insights to the field of fractional calculus. Several illustrative examples validate the method’s robustness and applicability. The approach enhances analytical capabilities for fractional differential equations, especially those with complex nonlinearities. This combined framework opens new avenues for solving a broader class of fractional equations. The essence of all this is that this technique is a new technique for solving Riccati’s fractional differential equations.
2020 Mathematical Sciences Classification: 34K10, 34K37, 35J05, 44A10, 47J35.
Keywords and Phrases: Adomian Decomposition Approach, Riccati’s Fractional Differential Equation and Kamal Integral Transform.