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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)
In this manuscript, a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm ‖x‖P d x, 0 , if there exist a, b, s and T : C → C satisfies the conditions 0 ≤ s |a| −2b < 2 a b and 4ad Tx, Ty b d x, Tx d y, Ty ≤ sd x, y for all x, y ∈(More)
We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend(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)