In this paper, we derive Haar wavelet operational matrix of the fractional integration and use it to obtain eigenvalues of fractional Sturm-Liouville problem. The fractional derivative is described in the Caputo sense. The efficiency of the method is demo nstrated by examples MSC: 26A33

In this paper, we derive Haar wavelet operational matrix of the fractional integration and use it to obtain eigenvalues of fractional Sturm-Liouville problem. The fractional derivative is described in the Caputo sense. The efficiency of the method is demonstrated by examples MSC: 26A33

In this study, fractional differential transform method (FDTM), which is a semi analytical-numerical technique, is used for computing the eigenelements of the Sturm-Liouville problems of fractional order. The fractional derivatives are described in the Caputo sense. Three problems are solved by the present method. The calculated results are compared closely with the results obtained by some exi...

‎In the present paper‎, ‎some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated‎. ‎Uniqueness theorems for the solution of the inverse problem are proved‎, ‎then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.

*Correspondence: [email protected] Department of Mathematics, Gaziosmanpasa University, Tasliciftlik Campus, Tokat, 60250, Turkey Abstract The main purpose of this study is to investigate a fractional discontinuous Sturm-Liouville problem with transmission conditions. We shall consider a fractional boundary value problem involving an operator with two parts. It is shown that the eigen...

The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, much progress has been recently achieved in both directions. objective this paper is to explore a different route, namely, construction explicit asymptotic approximations for solutions. As study case, we consider problem with left right Riemann-Liouville derivative...

‎In this paper‎, ‎we consider a new study about fractional $Delta$-difference equations‎. ‎We consider two special classes of Sturm-Liouville problems equipped with fractional $Delta$-difference operators‎. ‎In couple of steps‎, ‎the Lyapunov type inequalities for both classes will be obtained‎. ‎As application‎, ‎some qualitative behaviour of mentioned fractional problems such as stability‎, ‎...

This paper presents a method of numerically computing zeros of an analytic function for the specific application of computing eigenvalues of the Sturm-Liouville problem. The Sturm-Liouville problem is an infinite dimensional eigenvalue problem that often arises in solving partial differential equations, including the heat and wave equations. To compute eigenvalues of the Sturm-Liouville problem...