Publications Scientifiques
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Item Lyapunov- and Hartman-Type Inequalities for Generalized Caputo Fractional Differential Equations Incorporating Forcing Terms(John Wiley and Sons Ltd, 2025) Cherikh, Ouahiba; Adjabi, Yassine; Boulares, Hamid; Moumen, AbdelkaderIn this study, we construct the generalized Lyapunov- and Hartman-type inequalities for both linear and nonlinear generalized Caputo fractional differential equations under Dirichlet-type boundary conditions. By leveraging these inequalities, we can establish important results related to disconjugacy for the fractional differential equations. The inequalities we propose not only generalize but also enrich existing research in the literature, effectively addressing exceptional cases of fractional differential equationsItem Revisiting generalized Caputo derivatives in the context of two-point boundary value problems with the p-Laplacian operator at resonance(Springer Nature, 2023) Adjabi, Yassine; Jarad, Fahd; Bouloudene, Mokhtar; Panda, Sumati KumariThe novelty of this paper is that, based on Mawhin’s continuation theorem, we present some sufficient conditions that ensure that there is at least one solution to a particular kind of a boundary value problem with the p-Laplacian and generalized fractional Caputo derivative.Item Quasilinear coupled system in the frame of nonsingular ABC-derivatives with p-laplacian operator at resonance(Springer Nature, 2024) Bouloudene, Mokhtar; Jarad, Fahd; Adjabi, Yassine; Panda, Sumati KumariWe investigate the existence of solutions for coupled systems of fractional p-Laplacian quasilinear boundary value problems at resonance given by the Atangana–Baleanu–Caputo (shortly, ABC) derivatives formulations are based on the well-known Mittag-Leffler kernel utilizing Ge’s application of Mawhin’s continuation theorem. Examples are provided to demonstrate our findings.Item On abstract Cauchy problems in the frame of a generalized Caputo type derivative(DergiPark, 2023) Bourchi, Soumia; Jarad, Fahd; Adjabi, Yassine; Thabet, Abdeljawad; Mahariq, IbrahimIn 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 resultsItem 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, ThabetThis 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.Item On cauchy problems with caputo hadamard fractional derivatives(Kluwer Academic Publishers-Plenum Publishers, 2016) Adjabi, Yassine; Jarad, F.; Baleanu, D.; Abdeljawad, ThabetItem Third order rational ordinary differential equations with integer indices of fuchs(Springer, 2015) Adjabi, Yassine; Kessi, Arezki