There is global concern regarding the increased prevalence of math anxiety among college students, which is credited for a decrease in analytical degree completion rates and lower self-confidence among students in their ability to complete analytical tasks in the real world. The present study identified that, as expected, displays of instructional immediacy related positively to student intrinsic motivation and negatively to student math anxiety in analytical reasoning courses. More importantly, the findings were consistent with a mediated model in which psychological response to immediacy mediated the relationships between instructional immediacy cues and the associated outputs. Implications for theory and instruction are discussed.

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Abstract.Comparison results of the nonlinear scalar Riemann-Liouville fractional differential equation of order q, 0 < q ≤ 1, are presented without requiring Hölder continuity assumption. Monotone method is developed for finite systems of fractional differential equations of order q, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional differential system is proved.

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In this work we investigate integro-differential initial value problems with Riemann Liouville fractional derivatives where the forcing function is a sum of an increasing function and a decreasing function. We will apply the method of lower and upper solutions and develop two monotone iterative techniques by constructing two sequences that converge uniformly and monotonically to minimal and maximal solutions. In the first theorem we will construct two natural sequences and in the second theorem we will construct two intertwined sequences. Finally, we illustrate our results with an example.