This study portray the influence of variable viscosity, thermocapillarity, nonlinear convection, variable thermal conductivity on the laminar flow and heat transfer in a liquid film on a horizontal stretching sheet. Time dependent flow equations are transformed to coupled ordinary equations by the assistance of similarity transformation. Numerical results are obtained via applying Runge-kutta and Newton’s methods. For some representative value of the parameters graphs are exhibited and surface skin friction coefficient and heat transfer are presented in tabular form. It is observed that non-linear convection case shows higher velocity and associated boundary layer thickness compared with linear convection. Elapsed time is more in nonlinear convection for growing values of A, δ, Pr and M compared to linear convection.

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In this paper, we study the problem concerning meromorphic functions sharing a small function with weight l ≥ 0 and present one theorem which extends a results due to Zhang and Lü [19]

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In Nevanlinna's value distribution theory we considering some basic terms like T (r, f ), N (r, f ), m(r, f ) etc., and let f m (z) + q(z)[f n ∆ q η f ] (k) = p(z) be a non-linear q-th order difference equation and f (z) be a transcendental meromorphic function with finite order m, n and k be a positive integers such that m ≥ (q + 1)(nk + k + 2) + 3, p(z) be a meromorphic function satisfying N r, 1= S(r, f ). The q(z) be a non-zero meromorphic function satisfying that T (r, q(z)) = S(r, f ), then f (z) is not a solution of the non-linear q-th order difference equation. In this paper, we mainly investigate the uniqueness result of transcendental Fermat type q-shift equation by considering q-th order difference equation. Our result improves the results due to Abhijit Banerjee and Tania Biswas. In addition to that the example is exhibited to validate certain claims and justification of our main result. c f (z)), k ∈ N, k ≥ 2.