Numerical treatment by implementing a successive approximation method for fractional riccati and logistic differential equations

The fractional Riccati/Logistic differential equations (FRDE/FLDE) can be accurately solved numerically by using the approach presented in this study. In the provided questions, the fractional derivative is in the Caputo-Fabrizio (CF) sense. The suggested approach is the successive approximation technique (SAM). In this technique, we approximate the solution of the FRDE and FLDE with a finite-dimensional problem. A particular focus is examining the convergence analysis and estimating the upper bound on the error of the obtained approximate scheme. We offer an outcome on worldwide convergence of consecutive estimates. Also, to show the thoroughness of the method proposed, we computed the residual error function. Illustrative instances are given to prove the usefulness and validity of the suggested method.

---

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).