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This paper is concerned with the oscillation and asymptotic behavior of certain third-order nonlinear delay differential equations with distributed deviating arguments. By establishing sufficient conditions for the nonexistence of Kneser solutions and existing oscillation results for the studied equation, we obtain new criteria which ensure that every solution oscillates by using the theory of comparison with first-order delay equations and the technique of Riccati transformation. Some examples are presented to illustrate the importance of main results. [ABSTRACT FROM AUTHOR]

In this article, three different techniques, the Fractional Perturbation Iteration Method (FPIA), Fractional Successive Differentiation Method (FSDM), and Fractional Novel Analytical Method (FNAM), have been introduced. These three iterative methods are applied on different types of Electrical RLC-Circuit Equations of fractional-order. The fractional series approximation of the derived solutions can be established by using the obtained coefficients. These three algorithms handle the problems in a direct manner without any need for restrictive assumptions. The comparison displays an agreement between the obtained results. The beauty of this paper lies in the error analysis between the exact solution and approximate solutions obtained by these three methods which prove that the Approximate Solution obtained by FNAM converge very rapidly to the exact solution. [ABSTRACT FROM AUTHOR]

Due to the rapid development of theoretical and computational techniques in the recent years, the role of nonlinearity in dynamical systems has attracted increasing interest and has been intensely investigated. A study of nonlinear waves in shallow water is presented in this paper. The classic form of the Korteweg–de Vries (KdV) equation is based on oceanography theory, shallow water waves in the sea, and internal ion-acoustic waves in plasma. A shallow fluid assumption is shown in the framework by a sequence of nonlinear fractional partial differential equations. Indeed, the primary purpose of this study is to use a semi-analytical technique based on Fractional Taylor Series to achieve numerical results for nonlinear fifth-order KdV models of non-integer order. Caputo is the operator used for dealing with fractional derivatives. The generated solutions of nonlinear fifth-order KdV models of non-integer order for modeling turbulence processes in the field of ocean engineering are compared analytically and numerically, to demonstrate the behaviors of several parameters of the current model. We verified the method's convergence analysis and provided an error estimate by showing 2D and 3D graphs to further confirm its efficacy. [ABSTRACT FROM AUTHOR]

The main purpose of this research is to concentrate on the development of new definitions for the weighted geometric fractional integrals of the left-hand side and right-hand side of the function ℵ with regard to an increasing function used as an integral kernel. Moreover, the newly developed class of left-hand side and right-hand side weighted geometric fractional integrals of a function ℵ, by applying an additional increasing function, identifies a variety of novel classes as special cases. This is a development of the previously established fractional integrals by making use of the class of geometrically convex functions. Geometrically convex functions in weighted fractional integrals of a function ℵ in the form of another rising function yield the Hermite–Hadamard inequality type. We also establish a novel midpoint identity and the associated inequalities for a class of weighted fractional integral functions known as geometrically convex with respect to an increasing function and symmetric with respect to the geometric mean of the endpoints of the interval. In order to demonstrate the validity of our research, we present examples. Moreover, fractional inequalities and their solutions are applied in many symmetrical domains. [ABSTRACT FROM AUTHOR]

In this paper, we present some new refinement mappings associated with the Hermite–Hadamard type inequalities that are constructed for GA-convex mappings. Our investigation of the mappings leads to the discovery of several interesting features as well as the development of some inequalities for the Hermite–Hadamard type inequalities, which have already been established for GA-convex functions, as well as refining the relationship between the middle, rightmost, and leftmost elements of the function. Some applications to special means of positive real numbers are also given. [ABSTRACT FROM AUTHOR]