Newly Defined Conformable Derivatives

Motivated by a proportional-derivative (PD) controller, a more precise definition of a conformable derivative is introduced and explored. Results include basic conformable derivative and integral rules, Taylor’s theorem, reduction of order, variation of parameters, complete characterization of solutions for constant coefficient and Cauchy-Euler type conformable equations, Cauchy functions, variation of constants, a self-adjoint equation, and Sturm‐Liouville problems.