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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, whichdoi:10.12732/ijam.v32i5.9 fatcat:5r27couyqfafhfrhvw5re6xcvu