Abstract
In this paper, we consider sufficient conditions for the boundedness of every solution of fractional order fuzzy integral equations. Some examples are given to illustrate our results.
Highlights
The concept of fuzzy derivative was first introduced by Chang and Zadeh [1]
Authors considered the boundedness of solutions of the fuzzy differential equation x (t) = f t, x(t), t ∈ R+ = [0, +∞), (1.2)
The purpose of this paper is to investigate the boundedness of solutions of the following fuzzy functional integral equation with fractional order: t x(t) = (t – s)q–1 G1(t, s)x(s) + G2(t, s)x θ (s) ds + f (t), (1.3)
Summary
The concept of fuzzy derivative was first introduced by Chang and Zadeh [1]. Kaleva [2], Puri and Ralescu [3] introduced the notion of fuzzy derivative as an extension of the Hukuhara derivative and the fuzzy integral, which was the same as that proposed by Dubois and Prade [4]. It was proved in [9] that the boundedness of solutions of the following fuzzy integral equation: t x(t) = G(t, s)x(s) ds + f (t), (1.1) The purpose of this paper is to investigate the boundedness of solutions of the following fuzzy functional integral equation with fractional order: t x(t) = (t – s)q–1 G1(t, s)x(s) + G2(t, s)x θ (s) ds + f (t), (1.3)
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