Abstract
In recent years, fractional differential equations have emerged as powerful tools for modeling phenomena with memory and hereditary effects, owing to their non-local characteristics. These equations excel in tackling intricate problems across physics, engineering, and other fields. As analytical solutions are often infeasible, numerical methods play a vital role in their practical application. In this study, we have generalized Picard’s method to address fractional differential initial value problems with Caputo derivative, establishing an existence and uniqueness theorem applicable to both finite and infinite intervals. To substantiate our findings, we provide an example with graphical evidence demonstrating the convergence of the proposed method.
Recommended Citation
Mohan, Jag and Sood, Anju
(2050).
(R2159) A Novel Extension of Picard’s Method for Fractional Initial Value Problems with Convergence Analysis on Finite and Infinite Intervals,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 21,
Iss.
1, Article 18.
Available at:
https://digitalcommons.pvamu.edu/aam/vol21/iss1/18