Numerical investigation for Caputo-Fabrizio fractional Riccati and Bernoulli equations using iterative reproducing kernel method

Abstract

The pivotal aim of present work is to design and implement an effective numerical approach, the iterative reproducing-kernel algorithm, to provide numerical solutions to the fractional Riccati and Bernoulli differential equations in the Caputo-Fabrizio sense. To achieve this, we develop an advanced operational algorithm based on creating a complete orthonormal function system utilizing the reproducing-kernel function in order to formulate the solution in the form of uniformly convergent Fourier series. Additionally, error and stability analysis of the proposed method are studied in the appropriate space W2,2(Δ). On the other hand, some meaningful numerical applications are included to demonstrate the feasibility and reliability of this approach under the qualitative effect of the Caputo-Fabrizio fractional derivative. In numerical viewpoints, the achieved results using the proposed approach indicate a high level of accuracy and rare technical skills, which qualifies it to deal with many fractional models emerging in various mathematical and physical disciplines within the frame of Caputo-Fabrizio derivatives.