Search

For various conditions imposed on the parameters of the Horn hypergeometric function H4, we study different domains of convergence for the branched continued fraction expansions of the ratios of these functions. [ABSTRACT FROM AUTHOR]

The generalized nonlinear Schrödinger equation with M-truncated derivatives (GNLSE-MTD) is studied here. By using generalized Riccati equation and mapping methods, new elliptic, hyperbolic, trigonometric, and rational solutions are discovered. Because the GNLSE is widely employed in communication, heat pulse propagation in materials, optical fiber communication systems, and nonlinear optical phenomena, the resulting solutions may be used to analyze a wide variety of important physical phenomena. The dynamic behaviors of the various derived solutions are interpreted using 3-D and 2-D graphs to explain the affects of M-truncated derivatives. We can deduce that the surface shifts to the left when the order of M-truncated derivatives decreases. [ABSTRACT FROM AUTHOR]

The major objective of this article is to establish a new function called which is generalization of the generalized hypergeometric function and Mittag-Leffler function and obtain its properties particular differential property, integral representation, derivative formula and some integral transform, Euler transform, Laplace transform, Whittaker transform. We also derived the relations that exist between function with well known special functions. This article also deals with some fractional integral properties of the function using the Riemann–Liouville fractional integrals and derivatives operators. [ABSTRACT FROM AUTHOR]

For various conditions imposed on the parameters of the Horn hypergeometric function H4, we study different domains of convergence for the branched continued fraction expansions of the ratios of these functions. [ABSTRACT FROM AUTHOR]

The aim of this work is to improve the oscillation results for second-order neutral differential equations with damping term. We consider the noncanonical case which always leads to two independent conditions for oscillation. We are working to improve related results by simplifying the conditions, based on taking a different approach that leads to one condition. Moreover, we obtain different forms of conditions to expand the application area. An example is also given to demonstrate the applicability and strength of the obtained conditions over known ones. [ABSTRACT FROM AUTHOR]