Criteria of Existence for a q Fractional p-Laplacian Boundary Value Problem
, Lakhdar Ragoub* . 2020
This paper is devoted to establishing some criteria for the existence of non-trivial
solutions for a class of fractional q-difference equations involving the p-Laplace operator,
which is nowadays known as Lyapunov’s inequality. The method employed for it is
based on a construction of a Green’s function and its maximum value. Parallel to this
result, it is worth mentioning that the Hartman-Wintner inequality for the q-fractional
p-Laplace boundary value problem is also provided. It covers all previous results known
in the literature on the fractional case as well as that on the classical ordinary case. The
non-existence of non-trivial 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 an integral form of the solution construction of a
Green function corresponding to the considered problem and its properties as well as its
maximum value in consideration where the kernel is the Green’s function. The example
that we consider here for applying this result is an eigenvalue fractional problem. To be
more specific, we provide an interval where an appropriate Mittag-Leffler function to the
given eigenvalue fractional boundary problem has no real zeros.
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This paper is devoted to establishing some criteria for the existence of non-trivial
solutions for a class of fractional q-difference equations involving the p-Laplace operator,
which…