Using the reviewed Riemann-Liouville fractional derivative we define the bundle αk E = Osc(M) and highlight geometrical structures with a geometrical character. Also, we introduce the fractional osculator Lagrange space of k order and the main structures on it. The results are applied at the k order fractional prolongation of Lagrange, Finsler and Riemann fractional structures. Mathematics Subj...

This paper develops appropriate boundary conditions for the two-sided fractional diffusion equation, where the usual second derivative in space is replaced by a weighted average of positive and negative fractional derivatives. Mass preserving, reflecting boundary conditions for two-sided fractional diffusion involve a balance of left and right fractional derivatives at the boundary. Stable, con...

and Applied Analysis 3 Definition 2.2 see 18 . The standard Riemann-Liouville fractional derivative of order α > 0 of a continuous function y : a,∞ → R is given by D a y t 1 Γ n − α ( d dt )n ∫ t a t − s n−α−1y s ds, 2.2 where n α 1, provided that the integral on the right-hand side converges. Definition 2.3 see 18 . The Riemann-Liouville fractional integral of order α > 0 of a function y : a,∞...

The formulations of Riemann-Liouville and Caputo derivatives in the complex plane are presented. Two versions corresponding to the whole or half plane. It is shown that they can be obtained from the Grünwald-Letnikov derivative.

In this work, the authors study the existence of solutions for fractional differential inclusions in the sense of Almgren with Riemann-Liouville derivative. They also show the compactness of the solution set. A Peano type existence theorem is also proved.

In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle.

In this study, we obtained a system of eigenfunctions and eigenvalues for the mixed homogeneous Sturm-Liouville problem second-order differential equation containing fractional derivative operator. The differentiation operator was considered according to two definitions: Gerasimov-Caputo Riemann-Liouville-Visualizations eigenfunctions, biorthogonal system, distribution on real axis were present...

A new fractional subequation method is proposed for finding exact solutions for fractional partial differential equations (FPDEs). The fractional derivative is defined in the sense ofmodified Riemann-Liouville derivative. As applications, abundant exact solutions including solitary wave solutions as well as periodic wave solutions for the space-time fractional generalized Hirota-Satsuma coupled...