Faedo–Galerkin Approximation of Solution for a Nonlocal Neutral Fractional Differential Equation with Deviating Argument

详细信息    查看全文

• 作者：Alka Chadha ; Dwijendra N. Pandey
• 关键词：Analytic semigroup ; Banach fixed point theorem ; nonlocal conditions ; neutral fractional differential equation with deviating argument ; Faedo–Galerkin approximation
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：13
• 期：5
• 页码：3041-3067
• 全文大小：654 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

In this work, we study a class of nonlocal neutral fractional differential equations with deviated argument in the separable Hilbert space. We obtain an associated integral equation and then, consider a sequence of approximate integral equations. We investigate the existence and uniqueness of the mild solution for every approximate integral equation by virtue of the theory of analytic semigroup theory via the technique of Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. The Faedo–Galerkin approximation of the solution is studied and demonstrated some convergence results. Finally, we give an example.