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Uncertain fractional differential equations on a time scale under Granular differentiability concept

Authors: 

Ho Vu, Ngo Van Hoa*

Source title: 
Computational and Applied Mathematics, 38(3): 38-110, 2019 (ISI)
Academic year of acceptance: 
2018-2019
Abstract: 

In this work, the Caputo q-fractional initial value problem of order α ∈ (0,1) in uncertain environment is investigated. The uncertainties are considered as possibility sets using fuzzy sets. The concepts of horizontal membership function and granular difference are used to give a new definition for fuzzy fractional integral and derivative, called granular Riemann–Liouville q-fractional integral and granular Caputo q-fractional derivative. The existence and uniqueness of solution for the Caputo q-fractional initial value problem under granular differentiability concept is established. Finally, some illustrative examples are also presented.