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Citation - WoS: 6
Citation - Scopus: 8
On a Langevin Equation Involving Caputo Fractional Proportional Derivatives With Respect To Another Function
(Amer inst Mathematical Sciences-aims, 2022) Jarad, Fahd; Laadjal, Zaid
In this work, we introduce and study a class of Langevin equation with nonlocal boundary conditions governed by a Caputo fractional order proportional derivatives of an unknown function with respect to another function. The qualitative results concerning the given problem are obtained with the aid of the lower regularized incomplete Gamma function and applying the standard fixed point theorems. In order to homologate the theoretical results we obtained, we present two examples.
Citation - WoS: 4
Citation - Scopus: 4
Nonlinear Singular P-Laplacian Boundary Value Problems in the Frame of Conformable Derivative
(Amer inst Mathematical Sciences-aims, 2021) Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; Bouloudene, Mokhtar; Alqudah, Manar A.
This paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions.

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