IMA Journal of Applied Mathematics · 1987 · 590 citations · 0 references
Natural SciencesMathematicsPhysicsApplied MathematicsDifferential EquationsMathematical PhysicsFourier AnalysisOperator TheorySpectral TheoryFourier TransformFourier Transform TheoryFractional Differential EquationsOperational CalculusOperatorsOrdinary Differential Equation Systems
The objective of this paper is to make rigorous a formal study (Namias, 1980) of fractional powers for the Fourier transform. To make the theory unambiguous, it is found necessary to modify Namias's fractional operators. Some theorems are then proved for the modified operators and an operational calculus is developed. Finally, an application to an ordinary differential equation is considered.