Exact solution of a class of fractional integro‐differential equations with the weakly singular kernel based on a new fractional reproducing kernel space. (30th March 2018)

• Record Type: Journal Article
• Authors: Chen, Zhong; Wu, Longbin; Lin, Yingzhen
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 10(2018)
• Page Start: 3841
• Page End: 3855
• Publication Date: 2018-03-30
• Subjects: fractional integro‐differential equation -- fractional reproducing kernel space -- weakly singular kernel; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4870
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we construct a new fractional weighted reproducing kernel space, which is the minimum space containing the exact solution. The closed form of the reproducing kernel is obtained. Using this fractional reproducing kernel space, a class of fractional integro‐differential equations with a weakly singular kernel is solved. The error estimation is given. The final numerical experiments demonstrate the correctness of the theory and the effectiveness of the method.