Application of Rothe’s method to fractional differential equations
Authors :
D. Bahuguna 1 * and Anjali Jaiswal 2
Author Address :
1,2 Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur-208016, India.
*Corresponding author.
Abstract :
In this paper we consider an initial value problem for a fractional differential equation formulated in a Banach space $X$ where the fractional derivative is Riemann-Liouville type of order
$0<alpha<1$. We establish the existence and uniqueness of a strong solution of the problem by applying the method of semi-discretization in time, also known as the method of lines or more popularly as Rothe’s method. The dual space $X^{*}$ of $X$ is assumed to be uniformly convex. In the final section, we illustrate the applicability of the theoretical results with the help of an example.
Keywords :
Riemann-Liouville fractional derivative, Rothe’s method, Basset problem, accretive operator, strong solution.
DOI :
Article Info :
Received : December 24, 2018; Accepted : May 09, 2019.
