Abstract.   The Sturm-Liouville boundary value problem of the multi-order fractional differential equation  is studied. Results on the existence of solutions are established. The analysis relies on a weighted function space and a fixed point theorem. An example is given to illustrate the efficiency of the main theorems.

In this work, we study the following conformable fractional Sturm--Liouville
 problem
 \[
 l[y]=-T_{\alpha }(p(t)T_{\alpha }y(t))+q(t)y(t),
 \]
 where $t\in \lbrack 0,\infty ),$ real-valued functions $p$ and $q$
 satisfy conditions:
 \begin{array}{cc}
 (i) & q\in L_{\alpha }^{2}[0,\infty ), \\ 
 (ii) p\ \text{is\ absolutely\ continuous\ on}\ [0,\...

In this paper, we study the inverse problem for Sturm Liouville with conformable fractional differential operators of order and finite number interior discontinuous conditions. For aim first, asymptotic formulas solutions, eigenvalues eigenfunctions are calculated. Then some uniqueness theorems proposed eigenvalue proved. Finally, Hald's theorem 
 Sturm-Liouville is developed.

*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...

We develop an exponentially accurate fractional spectral collocation method for solving steady-state and time-dependent fractional PDEs (FPDEs). We first introduce a new family of interpolants, called fractional Lagrange interpolants, which satisfy the Kronecker delta property at collocation points. We perform such a construction following a spectral theory recently developed in [M. Zayernouri ...

As we know one of the most important equations which have many applications in various areas physics, mathematics, and financial markets, is Sturm–Liouville equation. In this paper, by using α-ψ-contraction technique fixed point theory employing some functional inequalities, study existence solutions partial fractional hybrid case generalized Sturm–Liouville-Langevin under boundary value condit...

We establish a generalization of Sturm–Picone comparison theorem for pair fractional nonlocal equations: $$\begin{aligned} (-div. (A_1(x)\nabla ))^{s} u= & {} C_{1}(x) u \,\,\,\text { in }\,\,\Omega ,\\ 0 \,\,\,\,\text on }\,\,\,\,\,\partial \Omega , \end{aligned}$$ and (A_2(x)\nabla v= C_{2}(x) v in}\,\,\Omega on}\,\,\,\,\,\partial where $$\Omega \subset \mathbb {R}^n$$ is an open bounded subs...

*Correspondence: [email protected] Department of Mathematics and Physical Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia Abstract In this article, we extend fractional calculus with nonsingular exponential kernels, initiated recently by Caputo and Fabrizio, to higher order. The extension is given to both left and right fractional derivatives and integrals. ...