Abstract
Fuzzy fractional differential equations (FFDEs) driven by Liu’s process are a type of fractional differential equations. In this paper, we intend to provide and prove a novel existence and uniqueness theorem for the solutions of FFDEs under local Lipschitz and linear growth conditions. We also investigate the stability of solutions to FFDEs by a theorem. Finally, some examples are provided.
Highlights
A large number of physical processes such as real-life phenomena appear to display fractional-order demeanor that may vary with space or time
We investigate the theory of fuzzy fractional differential equations (FDEs) (FFDEs) in the sense of Liu’s process
Weaker conditions are provided in order to guarantee the existence and uniqueness of the solution to the Fuzzy fractional differential equations (FFDEs), which makes it possible for more functions to be verified in such conditions
Summary
A large number of physical processes such as real-life phenomena appear to display fractional-order demeanor that may vary with space or time. We investigate the theory of fuzzy FDEs (FFDEs) in the sense of Liu’s process. ([ ]) The set function Cr is called a credibility measure if it satisfies the normality, monotonicity, self-duality, and maximality axioms. ([ ]) A fuzzy variable is defined as a (measurable) function ξ : ( , P, Cr) −→ R. ([ ]) Considering T to be an index set and ( , P, Cr) to be a credibility space, a fuzzy process can be described as a function from T × ( , P, Cr) to the set of real numbers. Every increment Ct+s – Cs is a normally distributed fuzzy variable with expected value et and variance σ t whose membership function is η(w) = + exp π√|w – et|.
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