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...

We consider in this paper approximation properties and applications of Mathieu functions. A first set of optimal error estimates are derived for the approximation of periodic functions by using angular Mathieu functions. These approximation results are applied to study the Mathieu-Legendre approximation to the modified Helmholtz equation and Helmholtz equation. Illustrative numerical results co...

All known finite sharply 4-transitive permutation sets containing the identity are groups, namely S4, S5, A6 and the Mathieu group of degree 11. We prove that a sharply 4-transitive permutation set on 11 elements containing the identity must necessarily be the Mathieu group of degree 11. The proof uses direct counting arguments. It is based on a combinatorial property of the involutions in the ...

The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapu...

Integral form expressions are obtained for the Mathieu-type series and their associated alternating versions, terms of which contain a (p,ν)-extended Gauss hypergeometric function. Contiguous recurrence relations found with respect to two parameters, finally, particular cases related bounding inequalities established.

Integral representations for generalised Mathieu series are obtained which recapture the Mathieu series as a special case. Bounds are obtained through the use of the integral representations.

For the first time, we attempted to define two new sub-classes of bi-univalent functions in open unit disc complex order involving Mathieu-type series, associated with generalized telephone numbers. The initial coefficients these classes were obtained. Moreover, also determined Fekete–Szegö inequalities for function and several related corollaries.