FUNCTIONAL ORDER DERIVATIVES AND THE $J^{\alpha_m}$ OPERATOR

R.H. France III, S. Careccia
2019 International Journal of Applied Mathematics  
The bulk of theoretical physics involves the solutions of differential equations, which are traditionally derived from a set of theoretical axioms. The authors consider the possibility that a function and its derivative are known, possibly from experimental results, while the order of the derivative is not. In most such cases there is no constant solution. The functional calculus approach to fractional derivatives is used to develop a definition of the J αm operator in one dimension, which
more » ... mension, which differentiates a function with a different order at each point in space.
doi:10.12732/ijam.v32i5.9 fatcat:5r27couyqfafhfrhvw5re6xcvu