Fractional Analogue of Sturm--Liouville Operator

In this paper we study a symmetric fractional differential operator of order $2\alpha$, ($1/2<\alpha<1$). Using the extension theory a class of self--adjoint problems generated by the fractional Sturm--Liouville equation is described.

2010 Mathematics Subject Classification: Primary 26A33; Secondary 34L10

Keywords and Phrases: Self--adjoint operator, symmetric operator, fractional Sturm--Liouville operator, fractional differential equation, boundary value problem, boundary condition, Caputo operator, Riemann--Liouville operator.

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