Delay Differential Equations of Fourth-Order: Oscillation and Asymptotic Properties of Solutions

Abstract

In this work, by using the comparison method and Riccati transformation, we obtain some oscillation criteria of solutions of delay differential equations of fourth-order in canonical form. These criteria complement those results in the literature. We give two examples to illustrate the main results. Symmetry plays an essential role in determining the correct methods for solutions to differential equations.

Qualitative Analysis of Langevin Integro-Fractional Differential Equation under Mittag–Leffler Functions Power Law

“…Due to its relevance in simulating numerous complicated events in various and widespread disciplines of science and engineering, fractional calculus (FC) and its applications have grown in importance over the last several decades. Some researchers noticed the need to develop the idea of fractional calculus by constructing new fractional derivatives (FD) with separate singular or nonsingular kernels to satisfy the requirement to simulate diverse real-life situations in science and engineering [1][2][3][4][5][6][7][8]. In the exponential kernel, Caputo and Fabrizio in [9] introduced a new type of FD.…”