Some Notes on Fractional Differential Equations
Year: 2025
Type: conference-paper
Abstract: Fractional differential equations are an extension of classical integer-order differential equations, where the derivatives are of non-integer order,typically denoted as α, where 0<α<1 or α >1. These equations have become increasingly important in the modeling of complex real-world systems,particularly in fields such as physics, engineering, biology, and economics. However, due to the inability to find analytical solutions for most of theequations encountered in these fields, researchers have begun to take an interest in questions related to the qualitative properties of these equations.Qualitative analysis allows researchers to understand the behavior of solutions without needing to find explicit solutions, which may be difficult orimpossible for many fractional differential equations. This approach includes investigating properties such as existence and uniqueness of solutions,stability, boundedness, oscillations, etc. Among these qualitative properties, oscillatory behavior stands out as an important characteristic.Therefore, this study focuses on the oscillatory behavior of the equations. First, the oscillatory behavior of nonlinear fractional differential equationsis examined in detail, and several theorems for these equations are presented.
Authors: Adiguzel, Hakan, Can, Engin
Institution: Sakarya Uygulamalı Bilimler Üniversitesi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224908892