Application of Rothe’s method to fractional differential equations

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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.



Article Info :

Received : December 24, 2018; Accepted : May 09, 2019.



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