Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 98Citation - Scopus: 112Analysis and Some Applications of a Regularized Ψ-Hilfer Fractional Derivative(Elsevier, 2022) Jajarmi, Amin; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Nieto, Juan J.The main purpose of this research is to present a generalization of Psi-Hilfer fractional derivative, called as regularized Psi-Hilfer, and study some of its basic characteristics. In this direction, we show that the psi-Riemann-Liouville integral is the inverse operation of the presented regularized differentiation by means of the same function psi. In addition, we consider an initial-value problem comprising this generalization and analyze the existence as well as the uniqueness of its solution. To do so, we first present an approximation sequence via a successive substitution approach; then we prove that this sequence converges uniformly to the unique solution of the regularized Psi-Hilfer fractional differential equation (FDE). To solve this FDE, we suggest an efficient numerical scheme and show its accuracy and efficacy via some real-world applications. Simulation results verify the theoretical consequences and show that the regularized Psi-Hilfer fractional mathematical system provides a more accurate model than the other kinds of integer- and fractional-order differential equations. (C) 2022 Elsevier B.V. All rights reserved.Article Citation - WoS: 30Citation - Scopus: 33Dynamics of Fractional Order Delay Model of Coronavirus Disease(Amer inst Mathematical Sciences-aims, 2022) Zhang, Lei; Rahman, Mati Ur; Ahmad, Shabir; Riaz, Muhammad Bilal; Jarad, FahdThe majority of infectious illnesses, such as HIV/AIDS, Hepatitis, and coronavirus (2019-nCov), are extremely dangerous. Due to the trial version of the vaccine and different forms of 2019-nCov like beta, gamma, delta throughout the world, still, there is no control on the transmission of coronavirus. Delay factors such as social distance, quarantine, immigration limitations, holiday extensions, hospitalizations, and isolation are being utilized as essential strategies to manage the outbreak of 2019-nCov. The effect of time delay on coronavirus disease transmission is explored using a non-linear fractional order in the Caputo sense in this paper. The existence theory of the model is investigated to ensure that it has at least one and unique solution. The Ulam-Hyres (UH) stability of the considered model is demonstrated to illustrate that the stated model's solution is stable. To determine the approximate solution of the suggested model, an efficient and reliable numerical approach (Adams-Bashforth) is utilized. Simulations are used to visualize the numerical data in order to understand the behavior of the different classes of the investigated model. The effects of time delay on dynamics of coronavirus transmission are shown through numerical simulations via MATLAB-17.Article Citation - WoS: 132Citation - Scopus: 158On a New and Generalized Fractional Model for a Real Cholera Outbreak(Elsevier, 2022) Ghassabzade, Fahimeh Akhavan; Nieto, Juan J.; Jajarmi, Amin; Baleanu, DumitruIn this paper, a new mathematical model involving the general form of Caputo fractional derivative is studied for a real case of cholera outbreak. Fundamental properties of the new model including the equilibrium points as well as the basic reproduction number are explored. Also, an efficient approximation scheme on the basis of product-integration rule is established to solve the new model. Several kernel functions for the general fractional derivative are tested, and the results are compared with the real data of a cholera outbreak in Yemen. As a consequence, we find a special case in which the aforesaid outbreak is described better, for the corresponding numerical simulations are closer to the real data than the other classical and fractional frameworks. Next, we apply the most realistic model to investigate the effect of vaccination on the considered cholera outbreak. Simulation results show that earlier vaccination could reduce the number of infected individuals effectively, so mortality would have been reduced considerably if the vaccination had been performed earlier. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).Article Citation - WoS: 111Citation - Scopus: 123Stability Analysis and System Properties of Nipah Virus Transmission: a Fractional Calculus Case Study(Pergamon-elsevier Science Ltd, 2023) Shekari, Parisa; Torkzadeh, Leila; Ranjbar, Hassan; Jajarmi, Amin; Nouri, Kazem; Baleanu, DumitruIn this paper, we establish a Caputo-type fractional model to study the Nipah virus transmission dynamics. The model describes the impact of unsafe contact with an infectious corpse as a possible way to transmit this virus. The corresponding area to the system properties, including the positivity and boundedness of the solution, is explored by using the generalized fractional mean value theorem. Also, we investigate sufficient conditions for the local and global stability of the disease-free and the endemic steady-states based on the basic reproduction number R0. To show these important stability features, we employ fractional Routh-Hurwitz criterion and LaSalle's invariability principle. For the implementation of this epidemic model, we also use the Adams-Bashforth-Moulton numerical method in a fractional sense. Finally, in addition to compare the fractional and classical results, as one of the main goals of this research, we demonstrate the usefulness of minimal unsafe touch with the infectious corpse. Simulation and comparative results verify the theoretical discussions.Article On Hilbert-Pachpatte Type Inequalities Within ?-Hilfer Fractional Generalized Derivatives(Amer inst Mathematical Sciences-aims, 2023) Baleanu, Dumitru; Basci, YaseminIn this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided psi-Hilfer fractional derivatives with the general kernel. Our results are a generalization of the inequalities of Pecaric ' and Vukovic ' [1]. Furthermore, using the specific cases of the psi-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting psi, a1, b1 and considering the limit of the parameters alpha and beta.Article Citation - WoS: 36Citation - Scopus: 36All Linear Fractional Derivatives With Power Functions' Convolution Kernel and Interpolation Properties(Pergamon-elsevier Science Ltd, 2023) Baleanu, Dumitru; Shiri, BabakOur attempt is an axiomatic approach to find all classes of possible definitions for fractional derivatives with three axioms. In this paper, we consider a special case of linear integro-differential operators with power functions' convolution kernel a(a)(t-s)b(a) of order a a (0,1). We determine analytic functions a(a) and b(a) such that when a-* 0+, the corresponding operator becomes identity operator, and when a-* 1- the corresponding operator becomes derivative operator. Then, a sequential operator is used to extend the fractional operator to a higher order. Some properties of the sequential operator in this regard also are studied. The singularity properties, Laplace transform and inverse of the new class of fractional derivatives are investigated. Several examples are provided to confirm theoretical achievements. Finally, the solution of the relaxation equation with diverse fractional derivatives is obtained and compared.Article Citation - WoS: 15Citation - Scopus: 18A New Fractional Sica Model and Numerical Method for the Transmission of Hiv/Aids(Wiley, 2021) Baleanu, Dumitru; Ullah, Malik Zaka; Zaka Ullah, MalikIn this research, a new SICA model is proposed in a fractional framework for the HIV/AIDS transmission dynamics. The new model involves a Caputo-type fractional derivative with a Mittag-Leffler function as its nonsingular kernel. In addition, the resultant fractional equations avoid dimensional mismatching by using an auxiliary parameter. Furthermore, the nonnegativity of the solution, the equilibrium points, and their stability are studied. Additionally, we implement the model by a powerful approximation scheme based on the product-integration rule. Comparative results with the real experimental observations, happened in Cape Verde Islands from 1987 to 2014, verify that the new fractional model is more efficient than the pre-existent classical model with ordinary time derivatives. More to the point, the fractional order itself provides a degree of flexibility affecting the performance of the model, which is helpful to exhibit the hidden features of the disease transmission in an accurate, appropriate manner.Article Citation - WoS: 35Citation - Scopus: 31Optimal Solutions for Singular Linear Systems of Caputo Fractional Differential Equations(Wiley, 2021) Baleanu, Dumitru; Dassios, IoannisIn this article, we focus on a class of singular linear systems of fractional differential equations with given nonconsistent initial conditions (IC). Because the nonconsistency of the IC can not lead to a unique solution for the singular system, we use two optimization techniques to provide an optimal solution for the system. We use two optimization techniques to provide the optimal solution for the system because a unique solution for the singular system cannot be obtained due to the non-consistency of the IC. These two optimization techniques involve perturbations to the non-consistent IC, specifically, an l(2) perturbation (which seeks an optimal solution for the system in terms of least squares), and a second-order optimization technique at an l(1) minimum perturbation, (which includes an appropriate smoothing). Numerical examples are given to justify our theory. We use the Caputo (C) fractional derivative and two recently defined alternative versions of this derivative, the Caputo-Fabrizio (CF) and the Atangana-Baleanu (AB) fractional derivative.Article Citation - WoS: 17Citation - Scopus: 18On a Nonlocal Problem for a Caputo Time-Fractional Pseudoparabolic Equation(Wiley, 2021) Hammouch, Zakia; Karapinar, Erdal; Tuan, Nguyen Huy; Nguyen, Anh TuanIn 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.Article Citation - WoS: 33Citation - Scopus: 35Nonlinear F-Contractions on B-Metric Spaces and Differential Equations in the Frame of Fractional Derivatives With Mittag-Leffler Kernel(Pergamon-elsevier Science Ltd, 2019) Jarad, Fahd; Karapinar, Erdal; Alqahtani, Badr; Fulga, AndreeaIn this manuscript, we aim to refine and characterize nonlinear F-contractions in a more general framework of b-metric spaces. We investigate the existence and uniqueness of such contractions in this setting. We discuss the solutions to differential equations in the setting of fractional derivatives involving Mittag-Leffler kernels (Atangana-Baleanu fractional derivative) by using nonlinear F-contractions that indicate the genuineness of the presented result. (C) 2019 Elsevier Ltd. All rights reserved.