Tables of Values of the Nield- Kuznetsov Functions of the Firstand Second Kind

Initial and Boundary Value Problems Involving the Inhomogeneous Generalized Airy’s Equations

“…In case of the generalized inhomogeneous Airy's equation with constant forcing function, Abu Zaytoon et al [5] expressed its general solution with the help of a generalized form of the Nield-Kuznetsov function), who also provided its series representation using series representations of the generalized Airy's functions discussed in [6]. For the case of generalized, inhomogeneous Airy's equation with variable forcing function, Alzahrani et al [7] have recently provided a general solution in terms of a generalized form of the…”

“…are the generalized Airy's functions of the first-and second-kind, respectively, [6], and ) ( y K n is the generalized Nield-Kuznetsov function of the second-kind, defined by, [7] …”

“…The generalized Airy's functions, given in equations (25) and (26), above, have been used by Alzahrani et al [3,7] to derive the following series expressions for the generalized Nield-Kuznetsov functions …”

http://www.theijes.com/papers/vol6-issue3/A0603010108.pdf

“…In particular, they showed that the inhomogeneous Weber ordinary differential equations (ODE) of the form wherein prime notation denotes ordinary differentiation with respect to the independent variable y, plays an important role in the study of transition layer introduced by Nield and Kuznetsov, [2]. Equation (1) and its more general forms have received considerable attention in the literature due to its many applications in mathematical physics, (cf. [3] and the references therein).…”

“…In a recent article, Alzahrani et al [1] discussed how Weber's differential equation can be used in modelling flow through porous layers with variable permeability. In particular, they showed that the inhomogeneous Weber ordinary differential equations (ODE) of the form wherein prime notation denotes ordinary differentiation with respect to the independent variable y, plays an important role in the study of transition layer introduced by Nield and Kuznetsov, [2].…”