Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems

Abstract

In the present work we study the oscillatory behavior of three dimensional α -fractional nonlinear delay differential system. We establish some sufficient conditions that will ensure all solutions are either oscillatory or converges to zero, by using the inequality technique and generalized Riccati transformation. The newly derived criterion are also used to establish a new class of systems with delay which are not covered in the existing study of literature. Further, we constructed some suitable illustrations.

Hille and Nehari Type Oscillation Criteria for Conformable Fractional Differential Equations

“…It is a natural extension of usual derivative and it is named as Conformable, because this operator preserves basic properties of classical derivative (see [6][7][8][9]). Since conformable fractional derivative (CFD) is a local and limit based operator, it quickly takes a place in application problems [10][11][12][13][14][15][16]. Comparison principles of Sturm's type will be derived for self-adjoint differential equations.…”

Interval Oscillation Criteria for Self-adjoint Alpha-Fractional Matrix Differential Systems with Damping

“…The fractional order differential equations have been used to model several physical phenomena emerging in various Physical sciences, Biological, Ecological, Economics and Financial mathematics. See, for example [1,8,10,11,14,20,21,[28][29][30]35] and the references cited therein.…”