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math.CA2018
A derivative concept with respect to an arbitrary kernel and applications to fractional calculus
Mohamed Jleli, Mokhtar Kirane, Bessem Samet
In this paper, we propose a new concept of derivative with respect to an arbitrary kernel-function. Several properties related to this new operator, like inversion rules, integrati…
math.CA2017★ 2 cited
Lyapunov and Hartman-Wintner type inequalities for a nonlinear fractional boundary value problem with generalized Hilfer derivative
Mokhtar Kirane, Berikbol T. Torebek
In this work, we obtain a Lyapunov-type and a Hartman-Wintner-type inequalities for a linear and a nonlinear fractional differential equation with generalized Hilfer operator subje…