A new generalized and sharp version of Jordan’s inequality is proved and it is applied in the improvement of the Yang Le inequality. Moreover, a mistake in the proof of sharpening Jordan’s inequality… (More)

This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity,… (More)

Let {an}n=1 be an increasing sequence of positive real numbers. Under certain conditions of this sequence we use themathematical induction and the Cauchymean-value theorem to prove the following… (More)

This paper deals with some new generalizations of Hardy’s integral inequalities. Some cases concerning whether the constant factors involved in these inequalities are best possible are discussed in… (More)

Values of λ are determined for which there exist positive solutions of the fourth-order singular boundary value problems { x (4)(t) = λ f (t, x(t)), t ∈ (0, 1), x(0) = x(1) = 0, x ′′(0) = x ′′(1) =… (More)

A study is made of partial differential equations with piecewise constant arguments. ’Boundary value problems for three types of equations are discussed delayed; alternately of advanced and retarded… (More)

Under certain assumptions on the nonlinear–nonhomogenous term f (t, u(t)) of ordinary differential equations associated with fourth order singular boundary value problems, we establish a necessary… (More)