Abstract
In this paper, we investigate the existence of positive solutions for the boundary value problem of nonlinear fractional differential equation with mixed fractional derivatives and p-Laplacian operator. Then we establish two smart generalizations of Lyapunov-type inequalities. Some applications are given to demonstrate the effectiveness of the new results.
Highlights
1 Introduction Lyapunov’s inequality [ ] has proved to be very useful in various problems related with differential equations; for examples, see [, ] and the references therein
5 Conclusions In this paper, we prove existence of positive solutions to a nonlinear fractional boundary value problem involving a p-Laplacian operator
A numerical example shows that the new results are efficient
Summary
Lyapunov’s inequality [ ] has proved to be very useful in various problems related with differential equations; for examples, see [ , ] and the references therein. Many researchers have given some Lyapunov-type inequalities for different classes of fractional boundary value problems (see [ – ]). In [ ], Ferreira investigated a Lyapunov-type inequality for the fractional boundary value problem Where Dαa+ is the Riemann-Liouville fractional derivative of order α, < α ≤ , a and b are consecutive zeros, and q is a real and continuous function.
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