Asymptotic and Oscillatory Properties of Noncanonical Delay Differential Equations

Abstract

In this work, by establishing new asymptotic properties of non-oscillatory solutions of the even-order delay differential equation, we obtain new criteria for oscillation. The new criteria provide better results when determining the values of coefficients that correspond to oscillatory solutions. To explain the significance of our results, we apply them to delay differential equation of Euler-type.

Editorial for the Special Issue “Operators of Fractional Calculus and Their Multidisciplinary Applications”

“…The geographical distribution of the contributors to this Special Issue is remarkably widely-scattered. Their contributions (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]) originated in many different countries on every continent of the world. The subject matter of these nineteen publications (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]) deals extensively with such topics as fractional-order complex Ginzburg-Landau equations, fractional modeling for the treatment of cancer by using radiotherapy, fractional-order fuzzy complex-valued neural networks, the fractal-fractional Michaelis-Menten enzymatic reaction model, fractional-calculus operators involving the (p, q)-extended Bessel and Bessel-Wright functions, fractional-order diffusion-wave equations, Abel integral equations and their fractional-order analogues, nonlinear integro-differential equations, fractionalorder investigations of a number of celebrated integral inequalities, such as those that are popularly called the Pólya-Szegö inequality, the Grüss inequality, the Hermite-Hadamard inequality, and so on.…”

“…In [8], the authors have studied a fractional-order logistic differential equation by making use of several appropriate limit relations. The authors in [9] derive some asymptotic properties of non-oscillatory solutions of the even-order delay differential equation, thereby deducing criteria for oscillation. The article in [10] considers and analyzes a large number of fractional-calculus operators that are accessible in the current literature.…”