On Liapunov-Type Inequality for Third-Order Differential Equations

Abstract

In this paper, a Liapunov-type inequality has been derived for a class of third-order differential equations of the form,where p is a real-valued continuous function on 0, ϱ . The nature of the distance between consecutive two zeros or three zeros has been studied with the help of the inequality.

Hartman-Wintner-Type Inequality for a Fractional Boundary Value Problem via a Fractional Derivative with respect to Another Function

“…Many other generalizations and extensions of inequality (3) exist in the literature; see, for instance, [7,[13][14][15][16][17][18][19][20][21][22] and references therein. Due to the positive impact of fractional calculus on several applied sciences (see, for instance, [23]), several authors investigated Lyapunov-type inequalities for various classes of fractional boundary value problems.…”

Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications

“…The ordinary discrete Lyapunov inequality is then confirmed as tends to 2 from the right not as in the case of the classical fractional difference as tends to 2 from the left [15]. For various fractional Lyapunov extensions we refer, for 2 Discrete Dynamics in Nature and Society example, to [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. All the authors there were motivated by the following theorem on ordinary Lyapunov inequality.…”

A Lyapunov-type inequality for a fractional q-difference boundary value problem

“…In [22], Lyapunov established the following result: This result has found several applications in various problems related with differential equations and, since then, there have been several results to improve and generalize Theorem 1.1 in many directions (see [2,5,6,7,8,13,14,15,20,22,24,25,26,30] and the references therein).…”