On a Non-Newtonian Calculus of Variations

The calculus of variations is a field mathematical analysis born in 1687 with Newton’s problem minimal resistance, which concerned the maxima or minima integral functionals. Finding solution such problems leads to solving associated Euler–Lagrange equations. subject has found many applications over centuries, e.g., physics, economics, engineering and biology. Up this moment, however, theory been confined approach calculus. As negative values admissible functions are not physically plausible, we propose here develop an alternative based on non-Newtonian first introduced by Grossman Katz period between 1967 1970, provides defined, from very beginning, for positive real numbers only, it (non-Newtonian) derivative that permits one compare relative changes dependent variable independent also positive. In way, introduce natural framework involving images. Our main result first-order optimality condition type. new complements standard nontrivial/multiplicative guaranteeing remains range. An illustrative example given.