Differential/Difference Equations

The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations

Oscillation of a time fractional partial differential equation

We consider a time fractional partial differential equation subject to the Neumann boundary condition. Several sufficient conditions are established for oscillation of solutions of such equation by using the integral averaging method and a generalized Riccati technique. The main results are illustrated by examples

Some New Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Damping Term

We are concerned with oscillation of solutions of a class of nonlinear fractional differential equations with damping term. Based on a generalized Riccati function and inequality technique, we establish some new oscillation criteria for it. Some applications are also presented for the established results

Almost Oscillatory Solutions of a Three-Dimensional Half-Linear Neutral differential System of the Second Order

في هذا البحث تمت دراسة التذبذب والسلوك المقارب لنظام تفاضلي محايد ثلاثي الأبعاد نصف خطي من الدرجة الثانية ، حيث تم تصنيف جميع الحلول غير المتذبذبة إلى 16 فئة مختلفة ، ومن ثم تم إعطاء الشروط الكافية لإثبات ذلك. أن معظم هذه الفئات غير نشطة وغير متواجدة ، أي فارغة ، أما بالنسبة للفئات الباقية ، فقد ثبت أن جميع حلولها المحدودة ، سواء كانت متذبذبة أو غير متذبذبة ، تتقارب إلى الصفر عندما  ، وكلها الحلول الغير مقيدة ، اما ان تكون متذبذبة أو غير متذبذبة تذهب إلى  عندما  يتم إعطاء بعض الأمثلة لتوضيح النتائج التي تم الحصول عليها.In this research, the oscillation and the asymptotic behavior of a half-linear three-dimensional neutral differential system of the second order have been studied, where all the non-oscillating solutions have been classified into 16 different classes, and then sufficient conditions were given to prove that most of these classes  are inactive and non-occurring, that is empty, as for the rest classes, it has been proven that all its bounded solutions, either oscillating or non-oscillating, converge to zero when , and all unbounded solutions, are either oscillating or non-oscillating, goes to  as . Some examples are given to illustrate the obtained result