with applications to fractional differential equations and science /
Carl F. Lorenzo, National Aeronautics and Space Administration, Glenn Research Center, Cleveland, Ohio, Tom T. Hartley, The University of Akron, Akron, Ohio
1611
1 online resource
Includes bibliographical references and index
The Fractional Exponential Function via the Fundamental Fractional Differential Equation -- The Generalized Fractional Exponential Function: The R-Function and Other Functions for the Fractional Calculus -- R-Function Relationships -- The Fractional Hyperboletry -- The R1-Fractional Trigonometry -- The R 2-Fractional Trigonometry -- The R 3-Trigonometric Functions -- The Fractional Meta-Trigonometry -- The Ratio and Reciprocal Functions -- Further Generalized Fractional Trigonometries -- The Solution of Linear Fractional Differential Equations Based on the Fractional Trigonometry -- Fractional Trigonometric Systems -- Numerical Issues and Approximations in the Fractional Trigonometry -- The Fractional Spiral Functions: Further Characterization of the Fractional Trigonometry -- Fractional Oscillators -- Shell Morphology and Growth -- Mathematical Classification of the Spiral and Ring Galaxy Morphologies -- Hurricanes, Tornados, and Whirlpools -- A Look Forward -- Related Works -- Computer Code -- Tornado Simulation -- Special Topics in Fractional Differintegration