In this article, we extend fractional operators with nonsingular Mittag-Leffler kernels, a study initiated recently by Atangana and Baleanu, from order [Formula: see text] to higher arbitrary order and we formulate their correspondent integral operators. We prove existence and uniqueness theorems for the Caputo ([Formula: see text]) and Riemann ([Formula: see text]) type initial value problems ...

this paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). in this problem q(x), d, a , b are real, qin l^2(0,pi), din(0,pi) and lambda is a parameter independent of x. by ...

We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.

We solve the inverse spectral problem for a class of Sturm–Liouville operators with singular nonlocal potentials and nonlocal boundary conditions.

We extend the idea of Jodeit and Levitan [3] for constructing isospectral problems of the classical scalar Sturm-Liouville differential equations to the vectorial Sturm-Liouville differential equations. Some interesting relations are found.

In this paper the existence of unique positive solutions for system (p,q,r)-Lapalacian Sturm-Liouville type two-point fractional order boundary vaue problems is established by an application n-fixed point theorem ternary operators on partially ordered metric spaces.

This research aims to accomplish an analytic solution mathematical models involving space-time fractional differential equations in the conformable sense series form through weighted inner product and separation of variables method. The main advantage this method is that various linear problems any kind can be solved by using First, corresponding eigenfunctions are established solving Sturm-Lio...

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