Conformable fractional Sturm‐Liouville equation

Abstract

In this article, we discuss a conformable fractional Sturm‐Liouville boundary‐value problem. We prove an existence and uniqueness theorem for this equation and formulate a self‐adjoint boundary value problem. We also construct the associated Green function of this problem, and we give the eigenfunction expansions. Finally, we will give some examples.

Two classes of conformable fractional Sturm‐Liouville problems: Theory and applications

“…Proposition 6.8. Fractional diffusion Equation (86) has a unique real-valued, weak solution, continuous in [0, ] × (0, ∞) obeying initial condition (87) and boundary conditions (88). The solution is given as series…”

“…[77][78][79] In recent years, many researchers have focused their attention on certain generalizations of Sturm-Liouville problems. [81][82][83][84][85][86][87][88] Existence and uniqueness theorems for fractional differential equations of conformable type are investigated in Gökdogan et al 83 In particular, a regular conformable fractional Sturm-Liouville eigenvalue problem was considered in Al-Rifae and Abdeljawad. 84 Mortazaasl and Jodayree Akbarfam in a previous study 86 presented the spectral theory for a conformable fractional Sturm-Liouville problem (CFSLP) and formulated a self-adjoint conformable fractional Sturm-Liouville operator (CFSLO) in a Hilbert space.…”

Criteria of limit‐point case for conformable fractional Sturm‐Liouville operators

“…It is also of great importance to investigate spectral properties of these differential operators. For recent results on conformable fractional calculus and the corresponding Sturm-Liouville equations, we refer the readers to Anderson and Ulness, 16 Al-Horani et al, 17 Al-Rifae and Abdeljawad, 18 Allahverdiev et al, 19 and Jarad et al 20 The papers of Abdeljawad et al 21 and Bas and Acay 22 are major in the Lyapunov inequalities for conformable boundary value problems. We note that there are other definitions such as the nonlocal fractional conformable derivatives generated by the local conformable ones given in Jarad et al 20 and Abdeljawad et al 23 In this paper, we consider the following 2 -order conformable fractional Sturm-Liouville operator:…”

Inverse problems for one dimensional conformable fractional Dirac type integro differential system

“…A variety of new results can be found ( [2], [3] and references therein). In recent years, scholars have focussed on a fractional generalization of the well known Sturm-Liouville and Dirac problems ( [4], [5], [6], [7], [8], [16], [27], [28] and [36]).…”