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In this paper, we study the existence of positive solutions for a class of coupled integral boundary value problems of nonlinear semipositone Hadamard fractional differential equations D α u(t) + λf (t, u(t), v(t)) = 0, D β v(t) + λg(t, u(t), v(t)) = 0, t ∈ (1, e), λ > 0, u (j) (1) = v (j) (1) = 0, 0 ≤ j ≤ n − 2, u(e) = µ e 1 v(s) ds s , v(e) = ν e 1 u(s)(More)
This paper studies a coupled system of nonlinear fractional differential equation with three-point boundary conditions. Applying the Schauder fixed point theorem, an existence result is proved for the following system D α u (t) = f (t, v (t) , D m v (t)) , t ∈ (0, 1) , D β v (t) = g (t, u (t) , D n u (t)) , t ∈ (0, 1) , u (0) = 0, D θ u (1) = δD θ u (η) , v(More)
Using Kosko's hypercube, we identify a fuzzy set with a point in a unit hypercube. A non-fuzzy or crisp subset of a set is a vertex of the hypercube. We introduce some new ideas: the definition of the fuzzy segment joining two given fuzzy subsets of a set, the set of midpoints between those two fuzzy subsets, and the set of equidistant points from given(More)
The purpose of this paper is to present a general view of the current applications of fuzzy logic in medicine and bioinformatics. We particularly review the medical literature using fuzzy logic. We then recall the geometrical interpretation of fuzzy sets as points in a fuzzy hypercube and present two concrete illustrations in medicine (drug addictions) and(More)
A concept of g-monotone mapping is introduced, and some fixed and common fixed point theorems for g-non-decreasing generalized nonlinear contractions in partially ordered complete metric spaces are proved. Presented theorems are generalizations of very recent fixed point theorems due to Agarwal et al. (2008).