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Iterative Hille-type oscillation criteria of half-linearadvanced dynamic equations of second order

In this paper, we establish iterative Hille-type criteria for advanced functionalhalf-linear dynamic equations of the second order. These results extend andimprove recent criteria established by multiple authors for the same equationand encompass classical criteria. We provide an example to demonstrate the significance of the results obtained.

Dynamical behavior of the fractional generalized nonlinear Schrödinger equation of third-order

The generalized nonlinear Schrödinger equation with M-truncated derivatives (GNLSEMTD) 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 fber communication systems, and nonlinear optical phenomena, the resulting solutions may be used to analyze a wide variety of important physical phenomena...

Second-Order Damped Differential Equations with Superlinear Neutral Term: New Criteria for Oscillation

This paper focuses on establishing new criteria to guarantee the oscillation of solutions for second-order differential equations with a superlinear and a damping term. New sufficient conditions are presented, aimed at analysing the oscillatory properties of the solutions to the equation under study. To prove these results, we employed various analysis methods, establishing new relationships to address certain problems that have hindered previous research. Consequently, by applying the princi...

NUMERICAL STABILITY OF THE BRANCHED CONTINUED FRACTION EXPANSION OF THE HORN’S HYPERGEOMETRIC FUNCTION H4

In this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions. The backward recurrence algorithm is one of the basic tools of computation approximants of branched continued fractions. Like most recursive processes, it is susceptible to error growth. Each cycle of the recursive process not only generates its own ro...

An approximation to Appell’s hypergeometric function F2 by branched continued fraction

Appell’s functions F1–F4 turned out to be particularly useful in solving a variety of problems in both pure and applied mathematics. In literature, there have been published a significant number of interesting and useful results on these functions. In this paper, we prove that the branched continued fraction, which is an expansion of ratio of hypergeometric functions F2 with a certain set of parameters, converges uniformly to a holomorphic function of two variables on every compact subset of ...

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