Interval oscillation criteria for impulsive conformable partial differential equations

G.E Chatzarakis,V Sadhasivam,T Raja,K Logaarasi

doi:10.2298/aadm180613006c

Abstract

In this paper, we present some sufficient conditions for the oscillation of all solutions of forced impulsive delay conformable partial differential equations. We consider two factors, namely impulse and delay that jointly affect the interval qualitative properties of the solutions of those equations. The results obtained in this paper extend and generalize some of the known results for forced impulsive conformable partial differential equations. An example illustrating the results is also given.

Highlights

Fractional differential equations are generalizations of the classical differential equations of integer order
For the theory and applications of fractional differential equations, we refer the reader to the monographs [14, 26]
Some key properties of the conformable derivative are summarized in the following Theorem

Summary

INTRODUCTION

Fractional differential equations are generalizations of the classical differential equations of integer order. For the theory and applications of fractional differential equations, we refer the reader to the monographs [14, 26]. Of particular interest is the work of Q.L. Li and W.S. Cheng [18] that established interval oscillation criteria, for a second order differential equation under impulse effects of the form n (p(t)x (t)) + q(t)x(t − τ ) + qi(t)Φαi (x(t − τ )) = e(t), t ≥ t0, i=1 x(t+k ) = akx(tk), x (t+k ) = bkx (tk), k = 1, 2, · · · , where 0 ≤ t0 < t1 < · · · < tk < · · · , lim tk = ∞, p, q, qi, e ∈ P LC([t0, ∞), R).

PRELIMINARIES

MAIN RESULTS

EXAMPLE

Conclusion