On Spectral Theory of Ordinary Differential Operator Of Fractional Order
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Date
2024-06-10
Journal Title
Journal ISSN
Volume Title
Publisher
Mohamed Boudiaf University of M'sila
Abstract
Fractional analysis is a branch of mathematical analysis which studies the possibility of defining noninteger powers of derivative and integrating operators. we define some useful functions such as
Gamma function, Beta function and MittagLeffler function. These functions play a very important
role in the theory of fractional order differential calculus. we will present the definition of a fractional
derivative and then we study the three most popular approaches to fractional derivatives: the
Grünwald-Letnikov, Riemann-Liouville and Caputo approaches as well as their properties. Finally, we
study some examples of fractional derivatives. Keywords: Fractional derivation, Grünwald-Letnikov,
Riemann-Liouville, Caputo. and operator theory to study the spectral properties (such as eigenvalues
and eigenfunctions) of fractional differential operators.
Description
Keywords
Closed Operator, spectrum, Differential of fractional order