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On abstract Cauchy problems in the frame of a generalized Caputo type derivative
(DergiPark, 2023) Bourchi, Soumia; Jarad, Fahd; Adjabi, Yassine; Thabet, Abdeljawad; Mahariq, Ibrahim
In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results
Nonlinear singular p -laplacian boundary value problems in the frame of conformable derivative
(American Institute of Mathematical Sciences, 2021) Bouloudene, Mokhtar; Alqudah, Manar A.; Fahd, Jarad; Adjabi, Yassine; Abdeljawad, Thabet
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.