TY - JOUR

T1 - Generalised fractional evolution equations of Caputo type

AU - Hernández-Hernández, M. E.

AU - Kolokoltsov, V. N.

AU - Toniazzi, L.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions. These results encompass known linear and non-linear equations from classical fractional partial differential equations such as the time-space-fractional diffusion equation, as well as their far reaching extensions. Meaning is given to a probabilistic generalisation of Mittag–Leffler functions.

AB - This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions. These results encompass known linear and non-linear equations from classical fractional partial differential equations such as the time-space-fractional diffusion equation, as well as their far reaching extensions. Meaning is given to a probabilistic generalisation of Mittag–Leffler functions.

KW - Boundary point

KW - Feller process

KW - Fractional evolution equation

KW - Generalised derivatives of Caputo type

KW - Mittag–Leffler functions

KW - Stopping time

KW - β-stable subordinator

UR - http://www.scopus.com/inward/record.url?scp=85020477396&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2017.05.005

DO - 10.1016/j.chaos.2017.05.005

M3 - Article

AN - SCOPUS:85020477396

VL - 102

SP - 184

EP - 196

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

ER -