Paper Info
Title
<Emphasis Type="Italic">q</Emphasis>-fractional differential equations with uncertainty
Abstract
In this paper, first we are going to introduce the fuzzy q-derivative and fuzzy q-fractional derivative in Caputo sense by using generalized Hukuhara difference, and then provide the related theorems and properties in detail. Moreover, the characterization theorem between the solutions of fuzzy Caputo q-fractional initial value problem (for short FCqF-IVP), which allows us to translate a FCqF-IVP and system of ordinary Caputo q-fractional differential equations (for short OCqF-DEs), is presented. In detail, the existence and uniqueness theorem is proved for the solution of FCqF-IVP. Finally, we restrict our attention to explain our idea for solving the FCqF-IVP and introducing its numerical solution by means of q-Mittag-Leffler function. The numerical examples demonstrate that the proposed idea is quite reasonable.
Year
DOI
Venue
2019
10.1007/s00500-019-03830-w
Soft Computing
Keywords
Field
DocType
Generalized Hukuhara difference, Fuzzy q-derivative, Fuzzy Caputo q-fractional derivative, Fuzzy Caputo q-fractional initial value problems, q-Krasnoselskii–Krein-type conditions, q-Mittag-Leffler function
Applied mathematics,Differential equation,Picard–Lindelöf theorem,Mathematical optimization,Computer science,Fuzzy logic,Initial value problem,restrict
Journal
Volume
Issue
ISSN
23.0
SP19.0
1433-7479
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Z. Noeiaghdam100.34
Tofigh Allahviranloo242641.47
Juan J. Nieto355981.45