The fractional trigonometry: with applications to fractional differential equations and science

Content: 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.