Browsing by Author "Adjabi, Yassine"

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Citation Count: Jarad, Fahd...et al. (2021). "Lyapunov type inequality in the frame of Generalized caputo derivatives", Discrete and Continuous Dynamical Systems - Series S, Vol. 14, No. 7, pp. 2335-2355.
Lyapunov type inequality in the frame of Generalized caputo derivatives
(2021) Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; Mallak, Saed F.; Alrabaiah, Hussam; 234808
In this paper, we establish the Lyapunov-type inequality for bound- A ry value problems involving generalized Caputo fractional derivatives that unite the Caputo and Caputo-Hadamrad fractional derivatives. An applica-tion about the zeros of generalized types of Mittag-Leffler functions is given. © 2021 American Institute of Mathematical Sciences. All rights reserved.
Citation Count: Bouloudene, Mokhtar...et al. (2021). "NONLINEAR SINGULAR p-LAPLACIAN BOUNDARY VALUE PROBLEMS IN THE FRAME OF CONFORMABLE DERIVATIVE", DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, Vol. 14, No. 10, pp. 3497-3528.
NONLINEAR SINGULAR p-LAPLACIAN BOUNDARY VALUE PROBLEMS IN THE FRAME OF CONFORMABLE DERIVATIVE
(2021) Bouloudene, Mokhtar; Alqudah, Manar A.; Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; 234808
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.
Citation Count: Bouloudene, Mokhtar...et al. (2021). "Nonlinear singular p-Laplacian boundary value problems in the frame of conformable derivative", Discrete and Continuous Dynamical Systems - Series S, Vol. 14, No. 10, pp. 3497-3528.
Nonlinear singular p-Laplacian boundary value problems in the frame of conformable derivative
(2021) Bouloudene, Mokhtar; Alqudah, Manar A.; Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; 234808
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. © 2021 American Institute of Mathematical Sciences. All rights reserved.
Citation Count: Bourchi, Soumia;...et.al. (2023). "On abstract Cauchy problems in the frame of a generalized Caputo type derivative", Advances in the Theory of Nonlinear Analysis and its Applications, Vol.7, No.1, pp.1-28.
On abstract Cauchy problems in the frame of a generalized Caputo type derivative
(2023) Bourchi, Soumia; Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; Mahariq, Ibrahim; 234808
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.
Citation Count: Adjabi, Y...et al. (2016). On Cauchy problems with Caputo Hadamard fractional derivatives. Journal of Computational Analysis and Application, 21(4), 661-681.
On Cauchy problems with Caputo Hadamard fractional derivatives
(Eudoxus Press, 2016) Adjabi, Yassine; Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet; 234808
The current work is motivated by the so-called Caputo-type modification of the Hadamard or Caputo Hadamard fractional derivative discussed in [4]. The main aim of this paper is to study Cauchy problems for a differential equation with a left Caputo Hadamard fractional derivative in spaces of continuously differentiable functions. The equivalence of this problem to a nonlinear Volterra type integral equation of the second kind is shown. On the basis of the obtained results, the existence and uniqueness of the solution to the considered Cauchy problem is proved by using Banach's fixed point theorem. Finally, two examples are provided to explain the applications of the results.
Citation Count: Jarad, Fahd...et al. (2018). On defining the distributions delta(r) and (delta ')(r) by conformable derivatives, Advances in Difference Equations.
On defining the distributions delta(r) and (delta ')(r) by conformable derivatives
(Springer Open, 2018) Jarad, Fahd; Adjabi, Yassine; Baleanu, Dumitru; Abdeljawad, Thabet; 56389; 234808
In this paper, starting from a fixed delta-sequence, we use the generalized Taylor's formula based on conformable derivatives and the neutrix limit to find the powers of the Dirac delta function delta(r) and (delta')(r) for any r is an element of R.
Citation Count: Adjabi, Yassine; Jarad, Fahd; Abdeljawad, Thabet, "On generalized fractional operators and a gronwall type ınequality with applications", Filomat, Vol.31, No.17, pp.5457-5473, (2017).
On generalized fractional operators and a gronwall type ınequality with applications
(Univ Nis, 2017) Adjabi, Yassine; Jarad, Fahd; Abdeljawad, Thabet; 234808
In this paper, we obtain the Gronwall type inequality for generalized fractional operators unifying Riemann-Liouville and Hadamard fractional operators. We apply this inequality to the dependence of the solution of differential equations, involving generalized fractional derivatives, on both the order and the initial conditions. More properties for the generalized fractional operators are formulated and the solutions of initial value problems in certain new weighted spaces of functions are established as well.
Citation Count: Bouloudene, Mokhtar...et al (2024). "Quasilinear Coupled System in the Frame of Nonsingular ABC-Derivatives with p-Laplacian Operator at Resonance", Qualitative Theory of Dynamical Systems, Vol. 23, no. 1.
Quasilinear Coupled System in the Frame of Nonsingular ABC-Derivatives with p-Laplacian Operator at Resonance
(2024) Bouloudene, Mokhtar; Jarad, Fahd; Adjabi, Yassine; Panda, Sumati Kumari; 234808
We 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.
Citation Count: Adjabi, Yassine;...et.al. (2023). "Revisiting generalized Caputo derivatives in the context of two-point boundary value problems with the p-Laplacian operator at resonance", Boundary Value Problems, Vol.2023, No.1.
Revisiting generalized Caputo derivatives in the context of two-point boundary value problems with the p-Laplacian operator at resonance
(2023) Adjabi, Yassine; Jarad, Fahd; Bouloudene, Mokhtar; Panda, Sumati Kumari; 234808
The 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.
Citation Count: Adjabi, Yasin...et.al. (2009). "Third order differential equations with fixed critical points", Applied Mathematics And Computation, Vol.208, No.1, pp.238-248.
Third order differential equations with fixed critical points
(Elsevier Science INC, 2009) Adjabi, Yassine; Jarad, Fahd; Kessi, Arezki; Mugan, Uğurhan; 234808
The singular point analysis of third order ordinary differential equations which are algebraic in y and y' is presented. Some new third order ordinary differential equations that pass the Painleve test as well as the known ones are found.