Browsing by Author "Hammouch, Zakia"

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Citation Count: Ullah, S...et al. (2020). "A Fractional Model for the Dynamics of Tuberculosis Infection Using Caputo-Fabrizio Derivative", Discrete and Continuous Dynamical Systems - Series S, Vol. 13, No. 3, pp. 975-993.
A Fractional Model for the Dynamics of Tuberculosis Infection Using Caputo-Fabrizio Derivative
(American Institute of Mathematical Sciences, 2020) Ullah, Saif; Khan, Muhammad Altaf; Farooq, Muhammad; Hammouch, Zakia; Baleanu, Dumitru; 56389
In the present paper, we study the dynamics of tuberculosis model using fractional order derivative in Caputo-Fabrizio sense. The number of confirmed notified cases reported by national TB program Khyber Pakhtunkhwa, Pakistan, from the year 2002 to 2017 are used for our analysis and estimation of the model biological parameters. The threshold quantity R0 and equilibria of the model are determined. We prove the existence of the solution via fixed-point theory and further examine the uniqueness of the model variables. An iterative solution of the model is computed using fractional Adams-Bashforth technique. Finally, the numerical results are presented by using the estimated values of model parameters to justify the significance of the arbitrary fractional order derivative. The graphical results show that the fractional model of TB in Caputo-Fabrizio sense gives useful information about the complexity of the model and one can get reliable information about the model at any integer or non-integer case. © 2020 American Institute of Mathematical Sciences. All rights reserve
Citation Count: Khader, M. M...et al. (2021). "A spectral collocation method for solving fractional KdV and KdV-Burgers equations with non-singular kernel derivatives", Applied Numerical Mathematics, Vol. 161, pp. 137-146.
A spectral collocation method for solving fractional KdV and KdV-Burgers equations with non-singular kernel derivatives
(2021) Khader, M. M.; Saad, Khaled M.; Hammouch, Zakia; Baleanu, Dumitru; 56389
The purpose of this paper is to investigate the spectral collocation method with help of Chebyshev polynomials. We consider the space fractional Korteweg-de Vries and the space fractional Korteweg-de Vries-Burgers equations based on the Caputo-Fabrizio fractional derivative. The proposed method reduces the models under study to a set of ordinary differential equations and then solves the system via the finite difference method. To the best our knowledge this is the first work which studies the Caputo-Fabrizio space fractional derivative for the proposed equations. The results were validated in the case of the classic differential equations in comparison with the exact solution and the calculation of the absolute error, and in the case of fractional differential equations, the results were verified by calculating the residual error function. In both cases, the results are very accurate and effective. The presented method is easy and accurate, and can be applied to many fractional systems. (c) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
Citation Count: Al-Qurashi, Maysaa...et al. (2021). "ACHIEVING MORE PRECISE BOUNDS BASED ON DOUBLE AND TRIPLE INTEGRAL AS PROPOSED BY GENERALIZED PROPORTIONAL FRACTIONAL OPERATORS IN THE HILFER SENSE", Fractals-Complex Geometry Patterns and Scaling in Nature and Society, Vol. 29, No. 05.
ACHIEVING MORE PRECISE BOUNDS BASED ON DOUBLE AND TRIPLE INTEGRAL AS PROPOSED BY GENERALIZED PROPORTIONAL FRACTIONAL OPERATORS IN THE HILFER SENSE
(2021) Al-Qurashi, Maysaa; Rashid, Saima; Karaca, Yeliz; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; 56389
A user-friendly approach depending on nonlocal kernel has been constituted in this study to model nonlocal behaviors of fractional differential and difference equations, which is known as a generalized proportional fractional operator in the Hilfer sense. It is deemed, for differentiable functions, by a fractional integral operator applied to the derivative of a function having an exponential function in the kernel. This operator generalizes a novel version of Cebysev-type inequality in two and three variables sense and furthers the result of existing literature as a particular case of the Cebysev inequality is discussed. Some novel special cases are also apprehended and compared with existing results. The outcome obtained by this study is very broad in nature and fits in terms of yielding an enormous number of relating results simply by practicing the proportionality indices included therein. Furthermore, the outcome of our study demonstrates that the proposed plans are of significant importance and computationally appealing to deal with comparable sorts of differential equations. Taken together, the results can serve as efficient and robust means for the purpose of investigating specific classes of integrodifferential equations.
Citation Count: Chand, Mehar...at all (2019). "Certain Fractional Integrals and Solutions of Fractional Kinetic Equations Involving the Product of S-Function", Mathematical Methods in Engineering: Applications in Dynamics of Complex Systems, Vol. 24, pp. 213-244.
Certain Fractional Integrals and Solutions of Fractional Kinetic Equations Involving the Product of S-Function
(2019) Chand, Mehar; Hammouch, Zakia; Asamoah, Joshua Kiddy K.; Baleanu, Dumitru; 56389
Citation Count: Khan, Muhammad Altaf; Hammouch, Zakia; Baleanu, Dumitru, "Modeling The Dynamics of Hepatitis E Via The Caputo-Fabrizio Derivative", Mathematical Modelling of Natural Phenomena, Vol. 14, No. 3, (2019).
Modeling The Dynamics of Hepatitis E Via The Caputo-Fabrizio Derivative
(EDP Sciences S A, 2019) Khan, Muhammad Altaf; Hammouch, Zakia; Baleanu, Dumitru; 56389
A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo-Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams-Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.
Citation Count: Jarad, Fahd...et al. (2020). "More properties of the proportional fractional integrals and derivatives of a function with respect to another function", Advances in Difference Equations, Vol. 2020, No. 1.
More properties of the proportional fractional integrals and derivatives of a function with respect to another function
(2020) Jarad, Fahd; Abdeljawad, Thabet; Rashid, Saima; Hammouch, Zakia; 234808
In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann–Liouville setting and the one in Caputo. In addition, we provide an integration by parts formulas related to the considered operators. © 2020, The Author(s).
Citation Count: Rashid, Saima...et al. (2020). "New estimates of integral inequalities via generalized proportional fractional integral operator with respect to another function", Fractals, Vol. 28, No. 8.
New estimates of integral inequalities via generalized proportional fractional integral operator with respect to another function
(2020) Rashid, Saima; Hammouch, Zakia; Jarad, Fahd; Chu, Yu-Ming; 234808
In this paper, the newly proposed concept of the generalized proportional fractional integral operator with respect to another function Φ has been utilized to generate integral inequalities using convex function. This new concept will have the option to reduce self-similitudes in the fractional attractors under investigation. We discuss the implications and other consequences of the integral inequalities concerning the generalized proportional fractional integral operator with respect to another function Φ are derived here and these outcomes permit us specifically to generalize some classical inequalities. Certain intriguing subsequent consequences of the fundamental hypotheses are also figured. It is to be supposed that this investigation will provide new directions in the quantum theory of capricious nature. © The Author(s)
Citation Count: Rashid, Saima...et al. (2020). "New generalizations in the sense of the weighted non-singular fractional integral operator", Fractals, Vol. 28, No. 8.
New generalizations in the sense of the weighted non-singular fractional integral operator
(2020) Rashid, Saima; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In this paper, we propose a new fractional operator which is based on the weight function for Atangana-Baleanu (AB)-fractional operators. A motivating characteristic is the generalization of classical variants within the weighted AB-fractional integral. We aim to establish Minkowski and reverse Hölder inequalities by employing weighted AB-fractional integral. The consequences demonstrate that the obtained technique is well-organized and appropriate. © 2020 The Author(s).
Citation Count: Rashid, Saima...et al. (2020). "New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating h-Convex Functions in Hilbert Space", Symmetry-Basel, Vol. 12, No. 2.
New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating h-Convex Functions in Hilbert Space
(2020) Rashid, Saima; Kalsoom, Humaira; Hammouch, Zakia; Ashraf, Rehana; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In Hilbert space, we develop a novel framework to study for two new classes of convex function depending on arbitrary non-negative function, which is called a predominating PLANCK CONSTANT OVER TWO PI-convex function and predominating quasiconvex function, with respect to eta, are presented. To ensure the symmetry of data segmentation and with the discussion of special cases, it is shown that these classes capture other classes of eta-convex functions, eta-quasiconvex functions, strongly PLANCK CONSTANT OVER TWO PI-convex functions of higher-order and strongly quasiconvex functions of a higher order, etc. Meanwhile, an auxiliary result is proved in the sense of kappa-fractional integral operator to generate novel variants related to the Hermite-Hadamard type for pth-order differentiability. It is hoped that this research study will open new doors for in-depth investigation in convexity theory frameworks of a varying nature.
Citation Count: Li, Yong-Min...et al. (2021). "NEW NEWTON'S TYPE ESTIMATES PERTAINING to LOCAL FRACTIONAL INTEGRAL VIA GENERALIZED p -CONVEXITY with APPLICATIONS", Fractals, Vol. 29, No. 5.
NEW NEWTON'S TYPE ESTIMATES PERTAINING to LOCAL FRACTIONAL INTEGRAL VIA GENERALIZED p -CONVEXITY with APPLICATIONS
(2021) Li, Yong-Min; Rashid, Saima; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; 56389
This paper aims to investigate the notion of p-convex functions on fractal sets α(0 < α ≤ 1). Based on these novel ideas, we derived an auxiliary result depend on a three-step quadratic kernel by employing generalized p-convexity. Take into account the local fractal identity, we established novel Newton's type variants for the local differentiable functions. Several special cases are apprehended in the light of generalized convex functions and generalized harmonically convex functions. This novel strategy captures several existing results in the relative literature. Application is obtained in cumulative distribution function and generalized special weighted means to confirm the relevance and computational effectiveness of the considered method. Finally, we supposed that the consequences of this paper can stimulate those who are interested in fractal analysis. © 2021 The Author(s).
Citation Count: Rashid, Saima...et al. (2020). "New quantum estimates in the setting of fractional calculus theory", Advances in Difference Equations, Vol. 2020, No. 1.
New quantum estimates in the setting of fractional calculus theory
(2020) Rashid, Saima; Hammouch, Zakia; Ashraf, Rehana; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this article, the investigation is centered around the quantum estimates by utilizing quantum Hahn integral operator via the quantum shift operator eta psi(q)(zeta) = q zeta + (1 - q)eta, zeta is an element of [mu, nu], eta = mu+ omega/(1-q), 0 < q < 1, omega >= 0. Our strategy includes fractional calculus, Jackson's q-integral, the main ideas of quantum calculus, and a generalization used in the frame of convex functions. We presented, in general, three types of fractional quantum integral inequalities that can be utilized to explain orthogonal polynomials, and exploring some estimation problems with shifting estimations of fractional order e(1) and the q-numbers have yielded fascinating outcomes. As an application viewpoint, an illustrative example shows the effectiveness of q, omega-derivative for boundary value problem.
Citation Count: Rashid, Saima...et al. (2021). "Novel aspects of discrete dynamical type inequalities within fractional operators having generalized (h)over-bar-discrete Mittag-Leffler kernels and application", CHAOS SOLITONS & FRACTALS, Vol. 151.
Novel aspects of discrete dynamical type inequalities within fractional operators having generalized (h)over-bar-discrete Mittag-Leffler kernels and application
(2021) Rashid, Saima; Sultana, Sobia; Hammouch, Zakia; Jarad, Fahd; Hamed, Y. S.; 234808
Discrete fractional calculus (DFC) has had significant advances in the last few decades, being successfully employed in the time scale domain (h) over barZ. Understanding of DFC has demonstrated a valuable improvement in neural networks and modeling in other terrains. In the context of Riemann form (ABTL), we discuss the discrete fractional operator influencing discrete Atangana-Baleanu (AB)-fractional operator having (h) over bar -discrete generalized Mittag-Leffler kernels. In the approach being presented, some new Polya-Szego and Chebyshev type inequalities introduced within discrete AB-fractional operators having h-discrete generalized Mittag-Leffler kernels. By analyzing discrete AB-fractional operators in the time scale domain Z, we can perform a comparison basis for notable outcomes derived from the aforesaid operators. This type of discretization generates novel outcomes for synchronous functions. The specification of this proposed strategy simply demonstrates its efficiency, precision, and accessibility in terms of the methodology of qualitative approach of discrete fractional difference equation solutions, including its stability, consistency, and continual reliance on the initial value for the solutions of many fractional difference equation initial value problems. The repercussions of the discrete AB-fractional operators can depict new presentations for various particular cases. Finally, applications concerning bounding mappings are also illustrated. (C) 2021 Elsevier Ltd. All rights reserved.
Citation Count: Jarad, Fand; Abdeljawad, Thabet; Hammouch, Zakia, "On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative", Chaos Solitons & Fractals, Vol. 117, pp. 16-20, (2018).
On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative
(Pergamon-Elsevier Science LTD, 2018) Jarad, Fahd; Abdeljawad, Thabet; Hammouch, Zakia; 234808
In this paper, we discuss the conditions of existence and uniqueness of solutions to a certain class of ordinary differential equations involving Atangana-Baleanu fractional derivative. Benefiting from the Gronwall inequality in the frame of Riemann-Liouville fractional integral, we establish a Gronwall inequality in the frame of Atangana-Baleanu fractional integral. Then, we study the stability of such equations in the sense of Ulam. (C) 2018 Elsevier Ltd. All rights reserved.
Citation Count: Nguyen, Anh Tuan...et al. (2021). "On a nonlocal problem for a Caputo time-fractional pseudoparabolic equation", Mathematical Methods in the Applied Sciences, Vol. 44, No. 18, pp. 14791-14806.
On a nonlocal problem for a Caputo time-fractional pseudoparabolic equation
(2021) Nguyen, Anh Tuan; Hammouch, Zakia; Karapınar, Erdal; Tuan, Nguyen Huy; 19184
In this paper, we consider a class of pseudoparabolic equations with the nonlocal condition and the Caputo derivative. Two cases of problems (1–2) will be studied, which are linear case and nonlinear case. For the first case, we establish the existence, the uniqueness, and some regularity results by using some estimates technique and Sobolev embeddings. Second, the Banach fixed-point theorem will be applied to the nonlinear case to prove the existence and the uniqueness of the mild solution.
Citation Count: Uddin, M. Farhad...et al. (2020). "Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness", Waves in Random and Complex Media.
Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness
(2020) Uddin, M. Farhad; Hafez, M. Golam; Hammouch, Zakia; Baleanu, Dumitru; 56389
The nonlinear Schrodinger equation (NLSE) in (2 + 1) dimensions with beta derivative evolution is considered here to study nonlinear coherent structures for Heisenberg models of ferromagnetic spin chain with magnetic exchanges. Such structures are studied by determining the analytical solutions of NLSE having beta derivative evolution via two different mathematical techniques. The dynamical behaviors of equilibrium points are also studied by deriving the planar dynamical system from the considered equation. Some of obtained analytical solutions are described with graphical representation by varying beta derivative parameter (BDP) and obliqueness. It is revealed that the obliqueness is extensively affected both on the plane wave dynamics as well as equilibrium points of the system, whereas the equilibrium points are independent of BDP.
Citation Count: Hammouch, Zakia; Baleanu, Dumitru; Melliani, Said (2021). "Preface: Special issue on recent advances in nonlinear dynamics and modelling", Discrete and Continuous Dynamical Systems - Series S, Vol. 14, No. 10, p.1.
Preface: Special issue on recent advances in nonlinear dynamics and modelling
(2021) Hammouch, Zakia; Baleanu, Dumitru; Melliani, Said; 56389
Citation Count: Singh, Jagdev;...et.al. (2021). "Recent advances in special functions, fractional operators and their real world applications", Mathematics in Engineering, Science and Aerospace, Vol.12, No.3, pp.631-634.
Recent advances in special functions, fractional operators and their real world applications
(2021) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra; Hammouch, Zakia; 56389
This special issue ”Recent Advances in Special Functions, Fractional Operators and their Real World Applications” of the journal Mathematics in Engineering, Science and Aerospace (MESA) is mainly collection of the research articles presented in 3rd International Conference on Mathematical Mod-elling, Applied Analysis and Computation (ICMMAAC-20) organized by the Department of Mathe-matics, JECRC University, Jaipur, India during August 7-9, 2020. This collection of articles is mainly concerned to address a wide range of special functions, operators of fractional order and their uses in mathematical modelling and computation of distinct problems of physical sciences, chemical sci-ences, biological sciences, engineering sciences, social science and economics. In the this special is-sue, expository and original research papers associated with the new trends and challenges in special functions and fractional order calculus and as well as their uses in real world problems are collected. Some are invited papers.
Citation Count: Rashid, Saima; Jarad, Fahd; Hammouch, Zakia (2021). "SOME NEW BOUNDS ANALOGOUS TO GENERALIZED PROPORTIONAL FRACTIONAL INTEGRAL OPERATOR WITH RESPECT TO ANOTHER FUNCTION", DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, Vol. 14, no. 10, pp. 3703-3718.
SOME NEW BOUNDS ANALOGOUS TO GENERALIZED PROPORTIONAL FRACTIONAL INTEGRAL OPERATOR WITH RESPECT TO ANOTHER FUNCTION
(2021) Rashid, Saima; Jarad, Fahd; Hammouch, Zakia; 234808
The present article deals with the new estimates in the view of generalized proportional fractional integral with respect to another function. In the present investigation, we focus on driving certain new classes of integral inequalities utilizing a family of positive functions n(n is an element of N) for this newly defined operator. From the computed outcomes, we concluded some new variants for classical generalized proportional fractional and other integrals as remarks. These variants are connected with some existing results in the literature. Certain interesting consequent results of the main theorems are also pointed out.