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1997•Kyungpook mathematical journalRequires access

Sturm-Liouville Equation of Fractional Order

Ahmed M. A. El-Sayed, Fatma M. Gaafar

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Abstract

In this work we define the Sturm-Liouville equation of fractional order and prove the continuation of it to the usual Sturm-Liouville equation. We study the initial value problem of the Sturm-Liouville equation of fractional order, and prove some properties of the solution. As an application we consider two eigenvalue problems of fractional differential operator.

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What this paper is about

In this work we define the Sturm-Liouville equation of fractional order and prove the continuation of it to the usual Sturm-Liouville equation. We study the initial value problem of the Sturm-Liouville equation of fractional order, and prove some properties of the solution. As an application we consider two eigenvalue problems of fractional differential operator.

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Available abstract

In this work we define the Sturm-Liouville equation of fractional order and prove the continuation of it to the usual Sturm-Liouville equation. We study the initial value problem of the Sturm-Liouville equation of fractional order, and prove some properties of the solution. As an application we consider two eigenvalue problems of fractional differential operator.

Key concepts: Sturm–Liouville theory, Mathematics, Continuation, Eigenvalues and eigenvectors, Order (exchange), Operator (biology), Fractional calculus, Differential equation

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