Analysis of Natural Daftardar–Jafari Method for Fractional Delay Differential Equations

• Published in: International journal of applied and computational mathematics 2024-06, Vol.10 (3), Article 117
• Main Authors: Mahatekar, Yogita, Deshpande, Amey S.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Computational Science and Engineering; Decomposition; Delay; Differential equations; Fractional calculus; Integral transforms; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Theoretical
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-024-01753-1

The decomposition methods such as Daftardar–Jafari method (DJM) have been applied previously to obtain a solution of the fractional differential equations. In the present article, we develop a decomposition method to solve fractional delay differential equations (FDDEs) using Natural Transform and Daftardar–Jafari method. This method is referred to as Natural Dafatardar Jafari Method (NDJM) for fractional delay differential equations. Further we perform a convergence analysis of NDJM for FDDEs and find the error bounds. We demonstrate NDJM for FDDEs with the help of various examples involving FDDEs and systems of FDDEs. We prove that the NDJM for FDDEs is more accurate than the contemporary integral transform methods, simplistic to implement yet more generalized than other transforms, and efficient in each case.