In this paper, we consider the existence of extreme solutions of the boundary value problem for a fractional order differential equation Dδu = f(t, u), t ∈ [0, T ], 0 < δ < 1, 0 < T < ∞, with a nonlinear boundary conditions g(u(0)) = u(T ). Under a lower solution α and un upper solution β with β ≤ α, we establish existence results of extreme solutions by means of the method of upper and lower s...

The problem of determining the sequence of a set of jobs with the objective function of minimizing the maximum earliness and tardiness in one machine is studied. Production systems like JIT are one of the many applications of the problem. This problem is studied in special cases and their optimal solutions are introduced with simple orders. In general, some effective conditions for neig...

In this paper, the method of lower and upper solutions is extended to deal with certain nonlinear fractional boundary value problem of order 3 < δ < 4. Two well-defined monotone sequences of lower and upper solutions which converge uniformly to actual solution of the problem are presented. The convergence of these sequences is verified numerically through one example and a result on the existen...

In this article, by using the technique of upper and lower solutions, some comparison results for first-order fuzzy differential equations are established. Hukuhara derivative, difference, partial orderings used proving theorems. We extend our to initial time difference case as well. Also, practicality these is demonstrated giving an example.

background: despite some successful dynamic simulation of self-impact double pendulum (sidp)-as humanoid robots legs or arms- studies, there is limited information available about the control of one leg locomotion. objective   : the main goal of this research is to improve the reliability of the mammalians leg locomotion and building more elaborated models close to the natural movements, by mod...