In this paper, we give some properties of the left and right finite Caputo derivatives. Such derivatives lead to finite Riesz type fractional derivative, which could be considered as the fractional power of the Laplacian operator modelling the dynamics of many anomalous phenomena in super-diffusive processes. Finally, the exact solutions of certain fractional diffusion partial differential equa...

connections between integral kernels of positivity preserving semigroups and suitable Lp contractivity properties are established. Then these questions are studied for the semigroups generated by -A + V and H,, the Dirichlet Laplacian for an open, connected region Q. As an application under a suitable hypothesis, Sobolev estimates are proved valid up to 352, of the form /n(x)1 ,< coo(x) lJHk,nl...

We study the Robin Laplacian in a domain with two corners of the same opening, and we calculate the asymptotics of the two lowest eigenvalues as the distance between the corners increases to infinity.

Using the improved lower bound on the sum of the eigenvalues of the Dirichlet Laplacian proved by A. D. Melas (Proc. Amer. Math. Soc. 131 (2003) 631-636), we report a new and sharp estimate for the dimension of the global attractor associated to the complex Ginzburg-Landau equation supplemented with Dirichlet boundary conditions.

one of the main goals of interpretation of gravity data is to detect location and edges of the anomalies. edge detection of gravity anomalies is carried out by different methods. terracing of the data is one of the approaches that help the interpreter to achieve appropriate results of edge detection. this goal becomes a complex task when the gravity anomalies have smooth borders due to gradual ...

We define and study two new kinds of “effective resistances” based on hubs-biased – hubs-repelling hubs-attracting models navigating a graph/network. prove that these effective resistances are squared Euclidean distances between the vertices graph. They can be expressed in terms Moore–Penrose pseudoinverse Laplacian matrices analogous Kirchhoff indices graph resistance distances. several result...

We provide an efficient method to calculate the pseudo-inverse of the Laplacian of a bipartite graph, which is based on the pseudo-inverse of the normalized Laplacian.

In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.

We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and Morley, for the largest eigenvalue of the Laplacian of an unweighted graph follows as a special ...