Papers by Abdelkader MOUMEN
Research Square (Research Square), Apr 18, 2023
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AIMS Mathematics
The approximate controllability of a class of fractional stochastic evolution equations (FSEEs) a... more The approximate controllability of a class of fractional stochastic evolution equations (FSEEs) are discussed in this study utilizes the Hilbert space by using Hilfer derivative. For different approaches, we remove the Lipschitz or compactness conditions and merely have to assume a weak growth requirement. The fixed point theorem, the diagonal argument, and approximation methods serve as the foundation for the study. The abstract theory is demonstrated using an example. A conclusion is given at the end.
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AIMS Mathematics
In this paper, we investigate the existence-uniqueness, and Ulam Hyers stability (UHS) of solutio... more In this paper, we investigate the existence-uniqueness, and Ulam Hyers stability (UHS) of solutions to a fractional-order pantograph differential equation (FOPDE) with two Caputo operators. Banach's fixed point (BFP) and Leray-alternative Schauder's are used to prove the existence- uniqueness of solutions. In addition, we discuss and demonstrate various types of Ulam-stability for our problem. Finally, an example is provided for clarity.
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AIMS Mathematics
In this work, we consider a nonlinear transmission problem in the bounded domain with a delay ter... more In this work, we consider a nonlinear transmission problem in the bounded domain with a delay term in the first equation. Under conditions on the weight of the damping and the weight of the delay, we prove general stability estimates by introducing a suitable Lyapunov functional and using the properties of convex functions.
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AIMS Mathematics
In the present manuscript, the BVP problem of a semipostone multipoint $ \Psi $-Caputo fractional... more In the present manuscript, the BVP problem of a semipostone multipoint $ \Psi $-Caputo fractional pantograph problem is addressed. \begin{document}$ \mathcal{D}_{r}^{\nu;\psi}\varkappa(\varsigma)+\mathcal{F}(\varsigma , \varkappa(\varsigma), \varkappa(r+\lambda\varsigma)) = 0, \ \varsigma \mbox{ in }(r, \mathcal{\Im}), $\end{document} \begin{document}$ \varkappa(r) = \vartheta_{1}, \ \varkappa(\mathcal{\Im}) = \sum\limits_{i = 1}^{m-2} \zeta_{i}\varkappa(\mathfrak{\eta}_{i})+\vartheta_{2}, \ \vartheta_{i} \in\mathbb{R}, \ i\in\{1, 2\}, $\end{document} and $ \lambda $ in $ \left(0, \frac{\mathcal{\Im}\mathfrak{-}r}{\mathcal{\Im} }\right) $. The seriousness of this research is to prove the existence of the solution of this problem by using Schauder's fixed point theorem (SFPT). We have developed our results in our research compared to some recent research in this field. We end our work by listing an example to demonstrate the result reached.
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Mathematics
In this paper, we investigate a new class of nonlinear fractional integrodifferential systems tha... more In this paper, we investigate a new class of nonlinear fractional integrodifferential systems that includes the Ψ-Riemann–Liouville fractional integral term. Using the technique of upper and lower solutions, the solvability of the system is examined. We add two examples to demonstrate and validate the main result. The main results highlight crucial contributions to the general theory of fractional differential equations.
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Symmetry
Integral inequalities are a powerful tool for estimating errors of quadrature formulas. In this s... more Integral inequalities are a powerful tool for estimating errors of quadrature formulas. In this study, some symmetric dual Simpson type integral inequalities for the classes of s-convex, bounded and Lipschitzian functions are proposed. The obtained results are based on a new identity and the use of some standard techniques such as Hölder as well as power mean inequalities. We give at the end some applications to the estimation of quadrature rules and to particular means.
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AIMS Mathematics
Navier-Stokes (NS) equations dealing with gravitational force with time-fractional derivatives ar... more Navier-Stokes (NS) equations dealing with gravitational force with time-fractional derivatives are discussed in this paper. These equations can be used to predict fluid velocity and pressure for a given geometry. This paper investigates the local and global existence and uniqueness of mild solutions to NS equations for the time fractional differential operator. We also work on the regularity effects of such types of equations were caused by orthogonal flow.
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Symmetry
Various scholars have lately employed a wide range of strategies to resolve specific types of sym... more Various scholars have lately employed a wide range of strategies to resolve specific types of symmetrical fractional differential equations. In this paper, we propose a new fractional identity for multiplicatively differentiable functions; based on this identity, we establish some new fractional multiplicative Bullen-type inequalities for multiplicative differentiable convex functions. Some applications of the obtained results are given.
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Symmetry
In this article, the fractional–space stochastic (2+1)-dimensional breaking soliton equation (SFS... more In this article, the fractional–space stochastic (2+1)-dimensional breaking soliton equation (SFSBSE) is taken into account in the sense of M-Truncated derivative. To get the exact solutions to the SFSBSE, we use the modified F-expansion method. There are several varieties of obtained exact solutions, including trigonometric and hyperbolic functions. The attained solutions of the SFSBSE established in this paper extend a number of previously attained results. Moreover, in order to clarify the influence of multiplicative noise and M-Truncated derivative on the behavior and symmetry of the solutions for the SFSBSE, we employ Matlab to plot three-dimensional and two-dimensional diagrams of the exact fractional–stochastic solutions achieved here. In general, a noise term that destroy the symmetry of the solutions increases the solution’s stability.
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Journal of Function Spaces
In this work, we examine a class of nonlinear neutral differential equations. Krasnoselskii’s fix... more In this work, we examine a class of nonlinear neutral differential equations. Krasnoselskii’s fixed-point theorem is used to provide sufficient conditions for the existence of positive periodic solutions to this type of problem.
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Symmetry
Multiplicative calculus, also called non-Newtonian calculus, represents an alternative approach t... more Multiplicative calculus, also called non-Newtonian calculus, represents an alternative approach to the usual calculus of Newton (1643–1727) and Leibniz (1646–1716). This type of calculus was first introduced by Grossman and Katz and it provides a defined calculation, from the start, for positive real numbers only. In this investigation, we propose to study symmetrical fractional multiplicative inequalities of the Simpson type. For this, we first establish a new fractional identity for multiplicatively differentiable functions. Based on that identity, we derive new Simpson-type inequalities for multiplicatively convex functions via fractional integral operators. We finish the study by providing some applications to analytic inequalities.
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Mathematics
This work presents a projection method based on Vieta–Lucas polynomials and an effective approach... more This work presents a projection method based on Vieta–Lucas polynomials and an effective approach to solve a Cauchy-type fractional integro-differential equation system. The suggested established model overcomes two linear equation systems. We prove the existence of the problem’s approximate solution and conduct an error analysis in a weighted space. The theoretical results are numerically supported.
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Mathematical and Computational Applications, 2021
In the present paper, we consider an important problem from the application perspective in scienc... more In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal conditions, placed on the nonlinear term and the relationship between the weights of the different damping mechanisms, are used to show the well-posedness of the solution using the semigroup theory. The solution energy has an explicit and optimal decay for the cases of equal and nonequal speeds of wave propagation.
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Open Mathematics, 2021
This article concerns linear one-dimensional thermoelastic Timoshenko system with memory and dist... more This article concerns linear one-dimensional thermoelastic Timoshenko system with memory and distributed delay terms where the Cattaneo law governs the heat flux q ( x , t ) q\left(x,t) . We proved an exponential stability result by using the energy method combined with Lyapunov functional.
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Mathematical and Computational Applications, 2021
The Korteweg–de Vries equation (KdV) is a mathematical model of waves on shallow water surfaces. ... more The Korteweg–de Vries equation (KdV) is a mathematical model of waves on shallow water surfaces. It is given as third-order nonlinear partial differential equation and plays a very important role in the theory of nonlinear waves. It was obtained by Boussinesq in 1877, and a detailed analysis was performed by Korteweg and de Vries in 1895. In this article, by using multi-linear estimates in Bourgain type spaces, we prove the local well-posedness of the initial value problem associated with the Korteweg–de Vries equations. The solution is established online for analytic initial data w0 that can be extended as holomorphic functions in a strip around the x-axis. A procedure for constructing a global solution is proposed, which improves upon earlier results.
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Optical Materials, 2021
Abstract Nanoparticles of BiVO3/g-C3N4 heterojunctions embedded two semiconductor of matching ban... more Abstract Nanoparticles of BiVO3/g-C3N4 heterojunctions embedded two semiconductor of matching band gap energy was employed for photodegradation of amaranth dye and evolution of huge amount of hydrogen gas. A simple thermal decomposition of urea is efficient route for producing g-C3N4 nanosheets. In ultrasonic bath of power intensity 150 Watt, BiVO3 nanoparticles were deposited homogeneously on g-C3N4 surface. The localization of BiVO3 nanoparticles on the corners of g-C3N4 sheets was proved with HRTEM analysis. With increasing BiVO3 contents to 10 wt%, the photocatalytic hydrogen evolution rate reach a maximum value of 6.8 mmolg−1h−1 which is ten fold higher than that of bare g-C3N4. The sonicated nanocomposites were characterized by XRD, N2-adsorption-desorption isotherm, HRTEM, XPS, DRS and PL. The influence of radiation power of ultrasound waves on the dye degradation and the amount of hydrogen evolved was established. The production of charge carriers with high reductive and oxidative power through step S-scheme mechanism is primary cause for the exceptional photocatalytic efficiency of the nanocomposites. The charge migration through step S-scheme mechanism rather than type (II) heterojunction mechanism was established by the PL measurements of terephthalic acid and the trapping scavengers experiments. Nanocomposite with 10 wt% BiVO3 possesses a superior reactivity for six consecutive cycles reveal the high stability of the as-synthesized sample.
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Multi-receiver encryption enables a sender to encrypt a message and transmit the ciphertext to a ... more Multi-receiver encryption enables a sender to encrypt a message and transmit the ciphertext to a set of authorized users, while no one out this group of authorized users can decrypt the message. Multi-receiver encryption is of great importance in many sectors such as broadcast communication, cloud computing, wireless communications, networking applications, e-voting, lottery, and medical applications. This paper proposes an efficient multi-receiver public key encryption scheme based on Lucas sequences. The results of the computational analysis show that, projected scheme is better against renown attacks and prevailing anonymous multireceiver algorithms
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Nonlinear Dynamics, 2015
The traffic of digital images has been quickly increased in the network. Security of image proces... more The traffic of digital images has been quickly increased in the network. Security of image processing became important for many sectors, namely for medical applications. Currently, the transmission of medical images is a daily routine. The large volume of data exchange has motivated the development of new methods to reduce the cost. Partial encryption is an approach to reduce the computational resources for huge volumes of multimedia. This paper introduces a new and secure approach, called graph coloring problem cryptography, to encrypt partially the medical images using the graph coloring problem (GCP). Before encrypting the medical images using advanced encryption standard algorithm, we use a GCP algorithm to localize and select some optimal positions of the pixels in the original images. Thus, the key of the cryptographic method is hard to be detected and extracted by the hackers. We get an acceptable percentage of the encrypted data for better security with a lower cost compared with the total image encryption.
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Nonlinear Engineering, 2017
Vulnerability of communication of digital images is an extremely important issue nowadays, partic... more Vulnerability of communication of digital images is an extremely important issue nowadays, particularly when the images are communicated through insecure channels. To improve communication security, many cryptosystems have been presented in the image encryption literature. This paper proposes a novel image encryption technique based on an algorithm that is faster than current methods. The proposed algorithm eliminates the step in which the secrete key is shared during the encryption process. It is formulated based on the symmetric encryption, asymmetric encryption and steganography theories. The image is encrypted using a symmetric algorithm, then, the secret key is encrypted by means of an asymmetrical algorithm and it is hidden in the ciphered image using a least significant bits steganographic scheme. The analysis results show that while enjoying the faster computation, our method performs close to optimal in terms of accuracy.
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Papers by Abdelkader MOUMEN