Approximations of Solutions of a Neutral Fractional Integro-Differential Equation

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• 作者：Alka Chadha ; Dwijendra N. Pandey
• 关键词：Analytic semigroup ; Banach fixed point theorem ; Caputo derivative ; Integro ; differential equation ; Faedo–Galerkin approximation
• 刊名：Differential Equations and Dynamical Systems
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：25
• 期：1
• 页码：117-133
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Engineering, general; Computer Science, general;
• 出版者：Springer India
• ISSN：0974-6870
• 卷排序：25

文摘

In the present work, we consider a fractional integro-differential equation in an arbitrary separable Hilbert space H. An associated integral equation and a sequence of approximate integral equations is studied. The existence and uniqueness of solutions to every approximate integral equation is obtained by using analytic semigroup and 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. We show the convergence of the solutions using Faedo–Galerkin approximation and demonstrate some convergence results. Finally, an example is considered to show the effectiveness of the obtained theory.