Document Type : Original Article
Authors
1
Khadri Khadkmaf P.O.-S.N.TEMPLE, RISHIKESH
2
School of Applied and Life Sciences, Uttaranchal University
3
School of Applied and Life Sciences, Uttaranchal University,
4
Department of Mathematics, CBIT,2P, Proddatur
5
Maharishi Markandeshwar (Deemed to be University), Mullana, India
6
Department of Science \& Humanities, GTU-Institute of technology and Research, Mehsana;
7
Lovely Professional University, Phagwara- 144411, Punjab India
8
Uttaranchal Institute of Technology (UIT), Uttaranchal University, Dehraudn 248007, Uttarakhand, India
9
DSB Campus Kumaun University Nainital
Abstract
This study presents a dual framework based on the Sumudu integral transform and Bell wavelet for solving a system of fractional differential equations (FDEs) under the Caputo derivative. The proposed framework enables both analytical and numerical treatment of the considered system of FDEs. The novelty of this work lies in the combined use of these two distinct, complementary techniques. The Sumudu transform yields analytical solutions in closed form through Mittag-Leffler functions for a system of FDEs by transforming the governing system into algebraic equations that are easier to handle. In parallel, the Bell wavelet approach provides highly accurate numerical approximations for a system of FDEs by exploiting the localization and approximation properties of wavelet basis functions. A convergence analysis is established to justify the reliability and stability of the proposed approach, and the theoretical estimates are supported by several numerical examples. The obtained results in the tables and figures confirm the good consistency between analytical and numerical results, and the performance is also compared against the Adams-Bashforth method (ABM). For integer-order, the approximate solutions obtained using the proposed approach show good agreement with those obtained by the classical fourth-order Runge-Kutta (RK4) method. All numerical simulations are carried out in Mathematica. The proposed dual-approach analysis can be readily extended to real-world systems in biology, physics, engineering, finance, and medicine where memory effects play a critical role. The results reveal that the hybrid framework is powerful, flexible, and promising for future development in the field of fractional modeling
Keywords
Subjects
