Generalized Fractional Nonlinear Birth Processes
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| 024 | 7 | 0 | |a 10.1007/s11009-013-9369-0 |2 doi |
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| 245 | 0 | 0 | |a Generalized Fractional Nonlinear Birth Processes |h [Elektronische Daten] |c [Mohsen Alipour, Luisa Beghin, Davood Rostamy] |
| 520 | 3 | |a We consider here generalized fractional versions of the difference-differential equation governing the classical nonlinear birth process. Orsingher and Polito (Bernoulli 16(3):858-881, 2010) defined a fractional birth process by replacing, in its governing equation, the first order time derivative with the Caputo fractional derivative of order υ ∈ (0, 1]. We study here a further generalization, obtained by adding in the equation some extra terms; as we shall see, this makes the expression of its solution much more complicated. Moreover we consider also the case υ ∈ (1, +∞ ), as well as υ ∈ (0, 1], using correspondingly two different definitions of fractional derivative: we apply the fractional Caputo derivative and the right-sided fractional Riemann-Liouville derivative on ℝ+, for υ ∈ (0, 1] and υ ∈ (1, +∞ ), respectively. For the two cases, we obtain the exact solutions and prove that they coincide with the distribution of some subordinated stochastic processes, whose random time argument is represented by a stable subordinator (for υ ∈ (1, +∞ )) or its inverse (for υ ∈ (0, 1]). | |
| 540 | |a Springer Science+Business Media New York, 2013 | ||
| 690 | 7 | |a Generalized fractional birth process |2 nationallicence | |
| 690 | 7 | |a Fractional Caputo derivative |2 nationallicence | |
| 690 | 7 | |a Fractional Riemann-Liouville derivative |2 nationallicence | |
| 690 | 7 | |a Mittag-Leffler functions |2 nationallicence | |
| 690 | 7 | |a Stable subordinator |2 nationallicence | |
| 700 | 1 | |a Alipour |D Mohsen |u Faculty of Basic Science, Babol University of Technology, P.O. Box 47148-71167, Babol, Iran |4 aut | |
| 700 | 1 | |a Beghin |D Luisa |u Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy |4 aut | |
| 700 | 1 | |a Rostamy |D Davood |u Department of Mathematics, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran |4 aut | |
| 773 | 0 | |t Methodology and Computing in Applied Probability |d Springer US; http://www.springer-ny.com |g 17/3(2015-09-01), 525-540 |x 1387-5841 |q 17:3<525 |1 2015 |2 17 |o 11009 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s11009-013-9369-0 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s11009-013-9369-0 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Alipour |D Mohsen |u Faculty of Basic Science, Babol University of Technology, P.O. Box 47148-71167, Babol, Iran |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Beghin |D Luisa |u Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Rostamy |D Davood |u Department of Mathematics, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Methodology and Computing in Applied Probability |d Springer US; http://www.springer-ny.com |g 17/3(2015-09-01), 525-540 |x 1387-5841 |q 17:3<525 |1 2015 |2 17 |o 11009 | ||