n this work, we establish some new oscillation results for the second-order nonlinear mixed neutral dynamic equation where. Our results not only complement and generalize some existing results in [4], but also can be applied to some oscillation problems that do not covered before, we also give some examples to illustrate our main results.

Two ways to efficiently construct a Non-Standard Finite Difference Method (NSFDM) is to approximate the nonlinear term(s) of the differential equation nonlocally and also to reconstruct the denominator function(s). In this research, we shall simulate a special class of nonlinear differential equations called the Riccati Differential Equations (RDEs) by nonlocally approximating the nonlinear terms and also reconstructing the denominator functions. The need for this approach came up due to some shortcomings of existing methods in which the qualitative properties of the exact solutions are not usually transferred to the numerical (approximate) solutions. The approach developed in this research has the property that its solution does not exhibit numerical instabilities in view of the results generated.

In this paper, a new analytical technique called Natural transform homotopy perturbation method has been successfully applied to obtain exact solution of nonlinear gas dynamic equation. Application of the method to three test modeling problems from mathematical physics lead to sequence which tends to the exact solution of the problems. The solution procedure shows the reliability of the method and is high accuracy evident.

A wide class of second order linear autonomous delay differential equations with distributed type delay is considered. By the use of two distinet real roots of the corresponding characteristic equation, a new result on the behavior of the solutions is obtained.

In this paper, we extend the possibility intuitionistic fuzzy soft sets defining new operations in it and a few properties of these operations are studied. An application of the new operations have been shown using example. Moreover the possibility intuitionistic fuzzy soft relations on PIFSS have been defined and their properties are discussed. As an end point, the notation of mapping on possibility intuitionistic fuzzy soft classes is defined and some properties of possibility intuitionistic fuzzy soft images and inverse images have been investigated. Examples and counterexamples for these concepts have been illustrated.

A wide class of third order linear autonomous neutral delay differential equations with distributed type delays is considered. Anasymptotic result, a useful exponential estimate of the solutions, a stability criterion are established.