The 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finite number N of identical particles is introduced. We suggest a ”fractional elastic harmonic potential”, and obtain the N -periodic fractional Laplacian operator in the form of a power law matrix function for the finite chain (N arbitrary not necessarily large) in explicit form. In the limiting ...

When defining a differential operator, one often employs, besides ordinary derivatives, generalized derivatives, which appear in a natural way when considering extensions of differential operators defined on differentiable functions, and weak derivatives, related to the transition to the adjoint operator [9]. Derivatives of fractional and negative orders appear when the differentiation is defin...

The object of this paper is to establish a relation between the n-dimensional H transform involving the Weyl type ndimensional Saigo operator of fractional integration.

By using the coincidence degree theory, we consider the following 2m-point boundary value problem for fractional differential equationD 0 u t f t, u t , D α−1 0 u t , D α−2 0 u t e t , 0 < t < 1, I3−α 0 u t |t 0 0, Dα−2 0 u 1 ∑m−2 i 1 aiD α−2 0 u ξi , u 1 ∑m−2 i 1 biu ηi , where 2 < α ≤ 3, D 0 and I 0 are the standard Riemann-Liouville fractional derivative and fractional integral, respectively...

Abstract In this work, we consider the solvability of a fractional-order p -Laplacian boundary value problem on half-line where fractional differential operator is nonlinear and has kernel dimension equal to two. Due nonlinearity operator, Ge Ren extension Mawhin’s coincidence degree theory applied obtain existence results for at resonance. Two examples are used validate established results.

In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integral boundary conditions involving fractional deri...