Browsing by Author "Nieto, Juan J."

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Citation - WoS: 1
Citation - Scopus: 1
Advanced Topics in Dynamics of Complex Systems
(Hindawi Ltd, 2014) Ahmad, Bashir; Nieto, Juan J.; Machado, J. A. Tenreiro; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 94
Citation - Scopus: 109
Analysis and Some Applications of a Regularized Ψ-Hilfer Fractional Derivative
(Elsevier, 2022) Jajarmi, Amin; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Nieto, Juan J.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 124
Citation - Scopus: 150
On a New and Generalized Fractional Model for a Real Cholera Outbreak
(Elsevier, 2022) Ghassabzade, Fahimeh Akhavan; Nieto, Juan J.; Jajarmi, Amin; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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/).
Citation - WoS: 164
Citation - Scopus: 175
A Survey on Fuzzy Fractional Differential and Optimal Control Nonlocal Evolution Equations
(Elsevier, 2018) Baleanu, Dumitru; Nieto, Juan J.; Torres, Delfim F. M.; Zhou, Yong; Agarwal, Ravi P.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered. (C) 2017 Elsevier B.V. All rights reserved.