In this article, we investigate upper and lower solutions to a system of coupled nonlinear fractional differential equations with multi-point coupled boundary conditions. Using monotone type iterative techniques combined with the upper and lower solutions method, some necessary and sufficient conditions are developed to guarantee existence of multiple solutions of the problem. The main result i...

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. &#10 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 ne...

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...

The notion of causal operators is extended to periodic boundary value problems with nonlinear boundary conditions in this paper. By utilizing the monotone iterative technique and the method of lower and upper solutions (resp. weakly coupled lower and upper solutions), we establish the existence of the extremal solutions (resp. weakly coupled extremal quasi-solutions) for nonlinear periodic boun...

In this paper, by using a monotone iterative technique in the presence of lower and upper solutions, we discuss the existence of solutions for a new system of nonlinear mixed type implicit impulsive integro-differential equations in Banach spaces. Under wide monotonicity conditions and the noncompactness measure conditions, we also obtain the existence of extremal solutions and a unique solutio...

symmetric division deg index is one of the 148 discrete adriatic indices that showed good predictive properties on the testing sets provided by international academy of mathematical chemistry.symmetric division deg index is defined by$$sdd(g) = sume left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right),$$where $d_i$ is the degree of vertex $i$ in graph $g$.in this pap...

this paper is devoted to the concepts of fuzzy upper and fuzzy lower contra-continuous multifunctions and also some characterizations of them are considered.