Classical mathematical models with a fractional approach
DOI:
https://doi.org/10.14393/BEJOM-v7-2026-79351Keywords:
Fractional calculus, Mittag-Leffler functions, Caputo fractional derivative, fractional differential equationsAbstract
In this work, we present an application of non-integer order differential calculus, known as Fractional Calculus, to classical mathematical models. We analyze the solution behavior of four problems involving fractional derivatives with initial conditions, which consists of replacing the usual derivative of the ordinary differential equation with a fractional derivative in the Caputo sense of a lower order than that of the original problem. The results of this work contribute to the field of modeling via non-integer order differential equations by investigating the behavior of their solutions. Such a contribution is particularly relevant given the lack of a well-defined physical interpretation for the fractional derivative, which makes the use of fractional models a challenging endeavor.
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