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International journal of computer mathematics, 2022-11, Vol.99 (11), p.2175-2204
Ort / Verlag
Abingdon: Taylor & Francis
Erscheinungsjahr
2022
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
-numbers are an ordered pair of fuzzy numbers used for formalization of imprecise and/or incomplete information. Basically, the concepts of
-numbers determine the reliability of information where the possibility distribution functions are taken into account. This theory has proved its potential and efficiency in modelling uncertain and complex phenomena by dynamical systems acting on both fuzziness and randomness environments. In this paper, we study an extension of fuzzy fractional differential equations to the
-numbers-valued domain, namely fractional
-differential equations. For this aim, we firstly introduce the concepts of Caputo fractional derivative and Riemann-Liouville fractional integral of
-number-valued-functions and prove the completeness of the metric space of
-number-valued-functions with some useful properties. Next, the fixed point approach is applied to investigate the existence and uniqueness of the integral solution of the initial value problem to fractional
-differential equations. At last, some stability problems for the proposed fractional
-differential equations are discussed, that is the stability in Hyers-Ulam sense of the initial value problem and the Lyapunov stability of the equilibrium point to the fractional
-differential equations. Some illustrating examples are given to demonstrate the correctness of theoretical results.