WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 14Citation - Scopus: 18Existence Theory and Numerical Simulation of HIV-I Cure Model with New Fractional Derivative Possessing a Non-Singular Kernel(Springeropen, 2019) Aliyu, Aliyu Lsa; Alshomrani, Ali Saleh; Li, Yongjin; Inc, Mustafa; Baleanu, DumitruIn this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana-Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard-Lindelof has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.Article Citation - WoS: 4Existence and Uniqueness of Solutions for a Nabla Fractional Boundary Value Problem With Discrete Mittag{leffler Kernel(inst Mathematics & Mechanics, Natl Acad Sciences Azerbaijan, 2021) Jonnalagadda, Jagan Mohan; Baleanu, Dumitru; Baleanu, Dumitru; MatematikWe consider a two-point boundary-value problem of order 1 < alpha < 3/2 involving nabla fractional differences with discrete Mittag-Leffler kernels. In [2], the authors obtained an expression for the Green's function of this boundary value problem. We determine an upper bound for the Green's function and derive a Lyapunov-type inequality. Further, we also establish sufficient conditions on existence and uniqueness of solutions for the corresponding nonlinear problem using fixed point theorems.Article Stability Analysis and Solutions of Fractional Boundary Value Problem on the Cyclopentasilane Graph(Cell Press, 2024) Wang, Guotao; Yuan, Hualei; Baleanu, DumitruThe study is being applied to a model involving silane and on cyclopentasilane graph. We consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of cyclopentasilane. In this paper, we first study the existence of solutions to fractional conformable boundary value problem on the cyclopentasilane graph by applying Scheafer and Krasnoselskii fixed point theorems. Furthermore, we investigate different kinds of Ulam stability such as Ulam-Hyers stable, generalized Ulam-Hyers stable, Ulam-Hyers-Rassias stable and generalized Ulam-HyersRassias stable for the given problem. Finally, we give an example to support our important results.Article Citation - WoS: 22Citation - Scopus: 26Impact of Public Health Awareness Programs on Covid-19 Dynamics: a Fractional Modeling Approach(World Scientific Publ Co Pte Ltd, 2023) Yusuf, Abdullahi; Musa, Salihu s.; Qureshi, Sania; Alshomrani, Ali s.; Baleanu, Dumitru; Zafar, Zain ul abadinPublic health awareness programs have been a crucial strategy in mitigating the spread of emerging and re-emerging infectious disease outbreaks of public health significance such as COVID-19. This study adopts an Susceptible-Exposed-Infected-Recovered (SEIR) based model to assess the impact of public health awareness programs in mitigating the extent of the COVID-19 pandemic. The proposed model, which incorporates public health awareness programs, uses ABC fractional operator approach to study and analyze the transmission dynamics of SARS-CoV-2. It is possible to completely understand the dynamics of the model's features because of the memory effect and hereditary qualities that exist in the fractional version. The fixed point theorem has been used to prove the presence of a unique solution, as well as the stability analysis of the model. The nonlinear least-squares method is used to estimate the parameters of the model based on the daily cumulative cases of the COVID-19 pandemic in Nigeria from March 29 to June 12, 2020. Through the use of simulations, the model's best-suited parameters and the optimal ABC fractional-order parameter t may be determined and optimized. The suggested model is proved to understand the virus's dynamical behavior better than the integer-order version. In addition, numerous numerical simulations are run using an efficient numerical approach to provide further insight into the model's features.Article Citation - WoS: 17Citation - Scopus: 19Results on Hilfer Fractional Switched Dynamical System With Non-Instantaneous Impulses(indian Acad Sciences, 2022) Malik, Muslim; Baleanu, Dumitru; Kumar, VipinThis paper concerns with the existence, uniqueness, Ulam's Hyer (UH) stability and total controllability results for the Hilfer fractional switched impulsive systems in finite-dimensional spaces. Mainly, this paper can be divided into three parts. In the first part, we examine the existence of a unique solution. In the second part, we establish the UH stability results, and in the third part, we study the total controllability results. The main outcomes are acquired by utilising the nonlinear analysis, fractional calculus, Mittag-Leffler function and Banach contraction principle. Finally, we have given two examples to validate the obtained analytical results.Article Citation - WoS: 34Citation - Scopus: 39Nonlinear Higher Order Fractional Terminal Value Problems(Amer inst Mathematical Sciences-aims, 2022) Shiri, Babak; Baleanu, DumitruTerminal value problems for systems of fractional differential equations are studied with an especial focus on higher-order systems. Discretized piecewise polynomial collocation methods are used for approximating the exact solution. This leads to solving a system of nonlinear equations. For solving such a system an iterative method with a required tolerance is introduced and analyzed. The existence of a unique solution is guaranteed with the aid of the fixed point theorem. Order of convergence for the given numerical method is obtained. Numerical experiments are given to support theoretical results.Article Hyers-Ulam Stability of Fractional Stochastic Differential Equations With Random Impulse(Korean Mathematical Soc, 2023) Baleanu, Dumitru; Kandasamy, Banupriya; Kasinathan, Ramkumar; Kasinathan, Ravikumar; Sandrasekaran, VarshiniThe goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.Article Citation - WoS: 7Citation - Scopus: 6On a Problem for the Nonlinear Diffusion Equation With Conformable Time Derivative(Taylor & Francis Ltd, 2022) Baleanu, Dumitru; Zhou, Yong; Huu Can, Nguyen; Au, Vo VanIn this paper, we study a nonlinear diffusion equation with conformable derivative: D-t((alpha)) u = Delta u = L(x, t; u(x, t)), where 0 < alpha < 1, (x, t) is an element of Omega x (0, T). We consider both of the problems: Initial value problem: the solution contains the integral I = integral(t)(0) tau(gamma) d tau (critical as gamma <= -1). Final value problem: not well-posed (if the solution exists it does not depend continuously on the given data). For the initial value problem, the lack of convergence of the integral I, for gamma <= -1. The existence for the solution is represented. For the final value problem, the Hadamard instability occurs, we propose two regularization methods to solve the nonlinear problem in case the source term is a Lipschitz function. The results of existence, uniqueness and stability of the regularized problem are obtained. We also develop some new techniques on functional analysis to propose regularity estimates of regularized solution.Article Citation - WoS: 14Citation - Scopus: 13Hilfer Fractional Neutral Stochastic Differential Equations With Non-Instantaneous Impulses(Amer inst Mathematical Sciences-aims, 2021) Kasinathan, Ravikumar; Baleanu, Dumitru; Annamalai, Anguraj; Kasinathan, RamkumarThe aim of this manuscript is to investigate the existence of mild solution of Hilfer fractional neutral stochastic differential equations (HFNSDEs) with non-instantaneous impluses. We establish a new criteria to guarantee the sufficient conditions for a class of HFNSDEs with non-instantaneous impluses of order 0 < beta < 1 and type 0 <= alpha <= 1 is derived with the help of semigroup theory and fixed point approach, namely Monch fixed point theorem. Finally, a numerical example is provided to validate the theoretical results.Article Citation - WoS: 5Citation - Scopus: 4Existence Results for Coupled Differential Equations of Non-Integer Order With Riemann-Liouville, Erdelyi-Kober Integral Conditions(Amer inst Mathematical Sciences-aims, 2021) Hemalatha, S.; Duraisamy, P.; Pandiyan, P.; Muthaiah, Subramanian; Baleanu, DumitruThis paper proposes the existence and uniqueness of a solution for a coupled system that has fractional differential equations through Erdelyi-Kober and Riemann-Liouville fractional integral boundary conditions. The existence of the solution for the coupled system by adopting the Leray-Schauder alternative. The uniqueness of solution for the problem can be found using Banach fixed point theorem. In order to verify the proposed criterion, some numerical examples are also discussed.