Pseudo-Processes Governed by Higher-Order Fractional Differential Equations
نویسندگان
چکیده
منابع مشابه
Pseudoprocesses governed by higher-order fractional differential equations
We study here a heat-type differential equation of order n greater than two, in the case where the time-derivative is supposed to be fractional. The corresponding solution can be described as the transition function of a pseudoprocess Ψn (coinciding with the one governed by the standard, non-fractional, equation) with a time argument Tα which is itself random. The distribution of Tα is presente...
متن کاملPoisson-type processes governed by fractional and higher-order recursive differential equations
We consider some fractional extensions of the recursive differential equation governing the Poisson process, i.e. d d t pk(t) =−λ(pk(t)− pk−1(t)), k ≥ 0, t > 0 by introducing fractional time-derivatives of order ν , 2ν , ..., nν . We show that the so-called “Generalized Mittag-Leffler functions” Ek α,β(x), x ∈ R (introduced by Prabhakar [24]) arise as solutions of these equations. The correspon...
متن کاملFractional Evolution Equations Governed by Coercive Differential Operators
and Applied Analysis 3 2. α-Times Regularized Resolvent Family Throughout this paper, X is a complex Banach space, and we denote by B X the algebra of all bounded linear operators on X. Let A be a closed densely defined operator on X, let D A and R A be its domain and range, respectively, and let α ∈ 0, 2 , C ∈ B X be injective. Define ρC A : {λ ∈ C : λ − A is injective and R C ⊂ R λ − A }. Let...
متن کاملOn boundary value problems of higher order abstract fractional integro-differential equations
The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...
متن کاملLinear Relaxation Processes Governed by Fractional Symmetric Kinetic Equations
We get fractional symmetric Fokker Planck and Einstein Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known kinetic equations of the Brownian motion theory and contain symmetric fractional derivatives over velocity and space, respectively. With the help of these equation...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2008
ISSN: 1083-6489
DOI: 10.1214/ejp.v13-496