ON USING VARIOUS MATHEMATICS INSTRUCTIONS VERSUS TRADITIONAL INSTRUCTION-AN ACTION RESEARCH

In this research, I provide an overview of potentially selected interactive mathematical instructions that help learners-educators identifying the most effective practices for teaching a course on differential equations. Based on my practical experience, positive and negative aspects of the used techniques are discussed. Immediate reactions on the disadvantages of the implementation of these different instructions have been successfully demonstrated throughout the practices. I conduct a survey in form of a questionnaire asking the learners about their opinions in this experience from which conclusion and recommendation are drawn and proposed to use in the process of teaching and learning next semesters.DOI: http://dx.doi.org/10.22342/jme.8.2.4139.133-14

Almost periodic solutions for an impulsive delay Nicholson’s blowflies model

AbstractBy means of the contraction mapping principle and Gronwall–Bellman’s inequality, we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay Nicholson’s blowflies model. The main results are illustrated by an example

Almost periodic solutions for Fox production harvesting model with delay

By utilizing the continuation theorem of coincidence degree theory, we shall prove that a Fox production harvesting model with delay has at least one positive almost periodic solution. Some preliminary assertions are provided prior to proving our main theorem. We construct a numerical example along with graphical representations to illustrate feasibility of the theoretical result

On the oscillatory behavior for a certain class of third order nonlinear delay difference equations

By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria for a certain class of third order nonlinear delay difference equations. Our results extend and improve some previously obtained ones. An example is worked out to demonstrate the validity of the proposed results

Oscillation of Nonlinear Third-Order Difference Equations with Mixed Neutral Terms

In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered

On the existence of positive solutions for generalized fractional boundary value problems

The existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of fixed point theorems. For the sake of converting the proposed problems into integral equations, we construct Green functions and study their properties for three different types of boundary value problems. Examples are presented to demonstrate the validity of theoretical findings.Scopu