A reproducing kernel method for nonlinear C-q-fractional IVPs. (March 2022)

• Record Type: Journal Article
• Authors: Yu, Yue; Niu, Jing; Zhang, Jian; Ning, Siyu
• Is Part Of: Applied mathematics letters. Volume 125(2022)
• Publication Date: 2022-03
• Subjects: C-q-fractional IVPs -- QNM -- RKM; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107751
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: Here a scheme for solving the Caputo type q-fractional (C-q-fractional) initial value problems (IVPs) in reproducing kernel spaces is given. By the attribute of the q-fractional operator, we first convert the q-fractional differential problems into q-fractional Volterra integral problems. Then, we implement the Quasi-Newton's method (QNM) to linearize the nonlinear equations. Finally, based on the theory of reproducing kernel method (RKM), a stable numerical scheme is proposed to resolve the linear equations. The reliability and efficiency are verified by numerical experiments.