A second order evolution equation with a lower order fractional term in a Banach space

Jaiswal, Anjali; Bahuguna, D.

doi:10.1063/1.5097512

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2019

2024

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Cited by 3 publications

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“…Many researchers adopted this method for solving various type of differential equations. The role of Rothe's method in the study of integer order and fractional order differential equations has been seen in various papers (see- [5], [3], [15], [4], [14], [16], [30]). This method has been well-founded as an efficient tool in solving partial differential equations and gives a numerical approach to find approximate solution.…”

Section: Introductionmentioning

confidence: 99%

Application of Rothe’s method to fractional differential equations

Bahuguna¹,

Jaiswal²

2019

Malaya J. Mat.

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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 < α < 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.

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