Using the concept of a fractional derivative, in Caputo’s sense, we derive and solve a fractional differential equation that models the deflection of beams. The scheme to introduce the fractional concept can be used for different situations; in the article, we only consider four cases as an example of its usefulness. In addition, we establish a relationship between the fractional index and the level of stiffness (or flexibility) of the material with which the beam is made.

Difficulties in mathematics are a significant cause of poor academic performance and high dropout rates in both secondary and higher education. This is often attributed to the abstract and disconnected way in which mathematical concepts are traditionally taught. To address this issue, this study proposes an innovative teaching strategy for introducing algebra through a collection of mathematical challenges aimed at beginner students. These challenges, including riddles, crossword puzzles, and adapted traditional board games, are designed to foster student interest, enhance logical thinking, and facilitate the teaching-learning process. The activities encourage students to actively construct their knowledge through hands-on, playful experiences. After administering the rally to 70 students, statistically significant differences were found between the pretest and posttest, leading to the conclusion that this rally can be an appropriate tool for promoting mathematical reasoning, hierarchy of operations, fractions, and algebraic equations.

In this article, we employ a fractional version of the radius of curvature in Euler’s equation for column buckling, enabling us to derive a fractional differential equation in the Caputo sense. We solve this equation and demonstrate that for certain values of the fractional parameter, there exists a critical buckling force. Additionally, we provide a numerical scheme for accurately approximating this critical force.