Fractional Integration and Differentiation of the Generalized Mathieu Series

Fractional Integration and Differentiation of the Generalized Mathieu Series

We aim to present some formulas for the Saigo hypergeometric fractional integral and differential operators involving the generalized Mathieu series Sμ(r), which are expressed in terms of the Hadamard product of the generalized Mathieu series Sμ(r) and the Fox–Wright function pΨq(z). Corresponding assertions for the classical Riemann–Liouville and Erdélyi–Kober fractional integral and different...

Accurate Approximation of a Generalized Mathieu Series

New, accurate lower and upper bounds for the sum of the generalized Mathieu series ∞ ∑ k=1 2k (k2 + x2) , p > 0,

A Numerical Integration Method by Using Generalized Series of Functions

Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation

A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional integration and differentiation, the Caputo fractional differentiation, the Riesz potential, and the Feller potential. It is also generalized f...

a numerical integration method by using generalized series of functions