In this paper, we discuss a class of new Volterra-Fredholm weakly singular difference inequality. The explicit bounds for the unknown functions are given clearly by discrete Jensen inequality, Cauchy-Schwarz inequality, Gamma function, change of variable, the mean-value theorem for integrals and amplification method. The derived results can be applied in the study of fractional difference equations in engineering.

In this paper, we discuss a class of new nonlinear weakly singular difference inequality, which is solved by change of variable, the mean-value theorem for integrals and amplification method, Gamma function, and explicit bounds for the unknown functions is given clearly.

In this paper, two new nonlinear difference inequalities are considered, where the inequalities consist of multiple iterated sums and composite function of nonlinear function and unknown function may be involved in each layer. Under several practical assumptions, the inequalities are solved through rigorous analysis, and explicit bounds for the unknown functions are given clearly. Further, the derived results are applied to the stability problem of a class of linear control systems with nonlinear perturbations.

Graduation practice is an indispensable part of college practice education, which is an important way to develop students’ practice and innovation capacity. In order to promote the quality of educating, as well as to achieve an effective management over graduation practice, this article will use Java language to design an institutionalized management system for college graduation practice. Advancing the efficiency and managerial level, the appliance of this system will bring forth good results.

In this paper, we discuss a class of new nonlinear weakly singular difference inequality. Using change of variable, discrete Jensen inequality, amplification method, the mean-value theorem for integrals and Gamma function, explicit bounds for the unknown functions in the inequality is given clearly. The derived results can be applied in the study of fractional difference equations in Engineering.