27 research outputs found
Subordination Pathways to Fractional Diffusion
The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and
under power law regime is splitted into three distinct random walks: (rw_1), a
random walk along the line of natural time, happening in operational time;
(rw_2), a random walk along the line of space, happening in operational
time;(rw_3), the inversion of (rw_1), namely a random walk along the line of
operational time, happening in natural time. Via the general integral equation
of CTRW and appropriate rescaling, the transition to the diffusion limit is
carried out for each of these three random walks. Combining the limits of
(rw_1) and (rw_2) we get the method of parametric subordination for generating
particle paths, whereas combination of (rw_2) and (rw_3) yields the
subordination integral for the sojourn probability density in space-time
fractional diffusion.Comment: 20 pages, 4 figure
Distributed-order wave equations with composite time fractional derivative
In this paper we investigate the solution of generalized distributed-order wave equations with composite time fractional derivative and external force, by using the Fourier-Laplace transform method. We represent the corresponding solutions in terms of infinite series in three parameter (Prabhakar), Mittag-Leffler and Fox H-functions, as well as in terms of the so-called Prabhakar integral operator. Generalized uniformly distributed-order wave equation is analysed by using the Tauberian theorem, and the mean square displacement is graphically represented by applying a numerical Laplace inversion algorithm. The numerical results and asymptotic behaviors are in good agreement. Some interesting examples of distributed-order wave equations with special external forces by using the Dirac delta function are also considered
ON SOME WEIGHTED HARDY-TYPE INEQUALITIES INVOLVING EXTENDED RIEMANN-LIOUVILLE FRACTIONAL CALCULUS OPERATORS
In this article, we establish some new weighted Hardy-type inequalities involving some variants of extended Riemann-Liouville fractional derivative operators, using convex and increasing functions. As special cases of the main results, we obtain the results of [18,19]. We also prove the boundedness of the k-fractional integral operator on L-p[a, b]