Construction of optical solitons for conformable generalized model in nonlinear media

In the current analysis, the conformable generalized Kudryashov equation of pulses propagation with power non-linearity is processed. The considered higher order equation represents a generalized mathematical model of many well-known ones in nonlinear media. A variety of multiple kinks, bi-symmetry, periodic, singular, bright and dark optical solitons are extracted via the generalized Riccati equation mapping method. Basing on the Riccati differential equation, the theoretical algorithm extracts a number of empirical solutions that do not exist in the literature. The obtained results showed that the present technique is an effective and strong tool for solving nonlinear fractional partial differential equations and produces a very large number of solutions.

On duality theory for multiobjective semi-infinite fractional optimization model using higher order convexity.

In the article, a semi-infinite fractional optimization model having multiple objectives is first formulated. Due to the presence of support functions in each numerator and denominator with constraints, the model so constructed is also non-smooth. Further, three different types of dual models viz Mond -Weir, Wolfe and Schaible are presented and then usual duality results are proved using higher-order [[EQUATION]] convexity assumptions. To show the existence of such generalized convex functions, a nontrivial example has also been exemplified. Moreover, numerical examples have been illustrated at suitable places to justify various results presented in the paper. The formulation and duality results discussed also generalize the well known results appeared in the literature.

Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line

In this paper, we consider a discontinuous, fully nonlinear, higher-order equation on the half-line, together with functional boundary conditions, given by general continuous functions with dependence on the several derivatives and asymptotic information on the (n−1)th derivative of the unknown function. These functional conditions generalize the usual boundary data and allow other types of global assumptions on the unknown function and its derivatives, such as nonlocal, integro-differential, infinite multipoint, with maximum or minimum arguments, among others. Considering the half-line as the domain carries on a lack of compactness, which is overcome with the definition of a space of weighted functions and norms, and the equiconvergence at ∞. In the last section, an example illustrates the applicability of our main result.

A Liouville theorem for the higher-order fractional Laplacian

We study Navier problems involving the higher-order fractional Laplacians. We first obtain nonexistence of positive solutions, known as the Liouville-type theorems, in the upper half-space [Formula: see text] by studying an equivalent integral form of the fractional equation. Then we show symmetry for positive solutions on [Formula: see text] through a delicate iteration between lower-order differential/pseudo-differential equations split from the higher-order equation.

Dynamics of Cracked Viscoelastic Beam: An Operator Based Finite Element Approach

The presence of crack introduces local flexibilities and changes physical characteristics of a structure which in turn alter its dynamic behavior. Crack depth, location, orientation and number of cracks are the main parameters that greatly influence the dynamics. Therefore, it is necessary to understand dynamics of cracked structures. Predominantly, every material may be treated as viscoelastic and most of the time material damping facilitates to suppress vibration. Thus present study concentrates on exploring the dynamic behavior of damped cantilever beam with single open crack. Operator based constitutive relationship is used to develop the general time domain, linear viscoelastic model. Higher order equation of motion is obtained based on Euler-Bernoulli and Timoshenko beam theory. Finite element method is utilized to discretize the continuum. Higher order equation is further converted to state space form for Eigen analysis. From the numerical results, it is observed that the appearance of crack decreases the natural frequency of vibration when compared to an uncracked viscoelastic beam. Under cracked conditions, the viscoelastic Timoshenko beam tends to give lower frequency values when compared to viscoelastic Euler-Bernoulli beam due to shear effect.