A new algorithm for fractional differential equation based on fractional order reproducing kernel space. (30th September 2020)

• Record Type: Journal Article
• Authors: Zhang, Ruimin; Lin, Yingzhen
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 2(2021)
• Page Start: 2171
• Page End: 2182
• Publication Date: 2020-09-30
• Subjects: complexity analysis -- convergence order -- fractional reproducing kernel space -- initial value problem of fractional equations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6927
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper develops an effective and new method to solve a class of fractional differential equations. The method is based on a fractional order reproducing kernel space. First, depending on some theories, a fractional order reproducing kernel space W α [0, 1] is constructed. The fractional order reproducing kernel space is a very suitable space to solve a class of fractional differential equations. Then, we calculate the reproducing kernel R y ( x ) of the space W α [0, 1] skilfully in §3. And convergence order and time complexity of this algorithm are discussed. We prove that the approximate solution u n of (1.1) converges to its exact solution u is not less than the second order. The time complexity of the algorithm is equal to the polynomial time of the third degree. Finally, three experiments support the algorithm strongly from the aspect of theory and technique.