Pseudo-Lucas Functions of Fractional Degree and Applications

Abstract

In a recent article, the first and second kinds of multivariate Chebyshev polynomials of fractional degree, and the relevant integral repesentations, have been studied. In this article, we introduce the first and second kinds of pseudo-Lucas functions of fractional degree, and we show possible applications of these new functions. For the first kind, we compute the fractional Newton sum rules of any orthogonal polynomial set starting from the entries of the Jacobi matrix. For the second kind, the representation formulas for the fractional powers of a r×r matrix, already introduced by using the pseudo-Chebyshev functions, are extended to the Lucas case.

The Comparative Study for Solving Fractional-Order Fornberg–Whitham Equation via ρ-Laplace Transform

“…In current years, fractional calculus (FC) applied in many phenomena in applied sciences, fluid mechanics, physics and other biology can be described as very effective using mathematical tools of FC. The fractional derivatives have occurred in many applied sciences equations such as reaction and diffusion processes, system identification, velocity signal analysis, relaxation of damping behaviour fabrics and creeping of polymer composites [5][6][7][8].…”

Fractional Hermite–Jensen–Mercer Integral Inequalities with respect to Another Function and Application

“…e theory of fractional integrals and derivatives has occurred in many fields and directions such as partial differential equations, difference equations, probability, and stochastic processes (see [1][2][3][4][5][6]). Behind it, the theory of convex functions with integral inequalities is also useful.…”