Abstract
We consider the oscillation of a class fractional differential equation with Robin and Dirichlet boundary conditions. By generalized Riccati transformation technique and the differential inequality method, oscillation criteria for a class of nonlinear fractional differential equation are obtained.
Highlights
The fractional differential equations are used to describe mathematical models of numerous real processes and phenomena studied in many areas of science and engineering such as population dynamics, neural networks, industrial robotics, electric circuits, optimal control, biotechnology, economics and many other branches of science
The oscillation theory as a part of the qualitative theory of differential equations has been developed rapidly in the last decades, and there has been a great deal of works on the oscillatory behavior of integer order differential equations [1] [2] [3]
As a new cross-cutting area, recently some attention has been paid to oscillations of fractional differential equations [4] [5] [6] [7]
Summary
The fractional differential equations are used to describe mathematical models of numerous real processes and phenomena studied in many areas of science and engineering such as population dynamics, neural networks, industrial robotics, electric circuits, optimal control, biotechnology, economics and many other branches of science. Some new developments in the oscillatory behavior of solutions of fractional differential equations with damping terms [8] [9] [10] [11] have been reported by authors. (H3) g-1 ∈ C(R; R) is continuous function with sg −1(s) > 0 for s ≠ 0 , there exists positive constant δ such that g −1(uv) ≤ δ g −1(u)g −1(v) for uv < 0 , and g −1(uv) ≥ δ g −1(u)g −1(v) for uv > 0. A solution u of (1.1) is said to be oscillatory if it is neither eventually positive nor eventually negative, otherwise it is nonoscillatory. Equation (1.1) is said to be oscillatory if all its solutions are oscillatory
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