Abstract
In this paper, we are concerned with the oscillatory behavior of a class of fractional differential equations with functional terms. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By using a variable transformation, a generalized Riccati transformation, Philos type kernels, and the averaging technique, we establish new interval oscillation criteria. Illustrative examples are also given.
Highlights
Differential equations of fractional order have recently been proved to be valuable tools in the modeling of many phenomena in various fields of science and engineering
Apart from diverse areas of mathematics, fractional differential equations arise in rheology, viscoelasticity, chemical physics, electrical networks, fluid flows, control, dynamical processes in self-similar and porous structures, etc
There have appeared lots of works in which fractional derivatives are used for a better description of considered material properties; mathematical modeling based on enhanced rheological models naturally leads to differential equations of fractional order and to the necessity of the formulation of initial conditions to such equations
Summary
Differential equations of fractional order have recently been proved to be valuable tools in the modeling of many phenomena in various fields of science and engineering. We are concerned with the oscillation of functional differential equations of fractional order in the form of Where Dαt (·) denotes the modified Riemann-Liouville derivative, the function r ∈ Cα([t , ∞), R+), which is the set of functions with continuous derivative or fractional order α, the function e ∈ C([t , ∞), R), the function ψ belongs to C(R, R) with < ψ(x) ≤ M for all x ∈ R and some M ∈ R+, the function F ∈ C([t , ∞) × R , R), and the function τ belongs to C([t , ∞), R+) with limt→∞ τ (t) = ∞.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
