In this paper, we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, the analytical solution for a class of fractional models associated with the logistic model, the von Foerster model and the Bertalanffy model is presented graphically for various fractional orders. The solution of the corresponding classical model is recovered as a particular case.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

Cryptography is present in everyday life and constitutes an essential tool to provide security and confidentiality in the transmission and deposit of information, based on knowledge and mathematical procedures. Thus, it is considered that it is a theme with the power to contextualize the teaching and learning process and to awaken students' interest in learning mathematical content. Thus, this work aims to present the use of cryptography as a tool to motivate the learning of the concept of function. The research, with a qualitative approach, was developed with 9th grade students from a municipal public school. Data were collected through questionnaires, observation and analysis of activities carried out by students. The use of the Inverted Classroom as a teaching methodology, added to the selected digital resources, contributed to the students' motivation to carry out the activities, presenting their understanding of the concept of function. Thus, it is expected that the results achieved can serve as a stimulus for more contextualized and meaningful teaching practices.

In this article, more general types of fractional operators with κ-deformed logarithm kernels are proposed. We analyse the new operators and prove various facts about them, including a semi group property. Results of existence are established in appropriate functional spaces. We prove that these results are valid at once for several standard fractional operators such as the Riemann-Liouville and Caputo operators, the Hadamard operators depending on the of the scaling function. We also show that our technique can beuseful to solve a wide range of Volterra integral equations. Finally, the solutions of theκ-fractional differential equations can be deduced from the solution representation of theCaputo or Riemann-Liouville versions via scaling.

A INTERMATHS publica artigos originais sobre as teorizações do campo da Matemática e sua interface com outras áreas do conhecimento, tais como Física, Engenharia, Biologia, Ciências Sociais, Economia e Educação Matemática.