AUTHOR=Ragoub Lakhdar , Tchier Fairouz , Tawfiq Ferdous 

TITLE=Criteria of Existence for a q Fractional p-Laplacian Boundary Value Problem

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 6 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2020.00007

DOI=10.3389/fams.2020.00007

ISSN=2297-4687

ABSTRACT=This paper is devoted to establish Lyapunov-type inequalities for a class of
fractional q-difference boundary value problem involving p-Laplace operator.
Also, it is worth to mention that the Hartman-Wintner inequality for the qfractional
p-Laplace boundary value problem is provided. The non existence
of non trivial of solutions to the q-difference fractional p-Laplace equation
subject to the Riemann-Liouville mixed boundary conditions will obey such
integral inequalities. The tools mainly rely on a construction of a Green
function corresponding to the considered problem, and its properties as well
as its maximum value. In order to illustrate this result, we provide an interval
where an appropriate Mittag-Leffler function to the given eigenvalue
fractional boundary problem has no real zeros.