WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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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 Hyers-Ulam Stability of Fractional Stochastic Differential Equations With Random Impulse(Comenius Univ, 2022) Varshini, S.; Banupriya, K.; Ramkumar, K.; Ravikumar, K.; Baleanu, D.; Kandasamy, Banupriya; Sandrasekaran, Varshini; Kasinathan, RamkumarThe goal of this study is to derive a class of random impulsive 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: 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 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: 13Citation - Scopus: 15A Study on K-Generalized ?-Hilfer Fractional Differential Equations With Periodic Integral Conditions(Wiley, 2024) Bouriah, Soufyane; Benchohra, Mouffak; Lazreg, Jamal Eddine; Karapinar, Erdal; Salim, AbdelkrimThis paper deals with some existence and uniqueness results for a class of problems systems for nonlinear k-generalized psi-Hilfer fractional differential equations with periodic conditions. The arguments are based on Mawhins coincidence degree theory. Furthermore, an illustration is presented to demonstrate the plausibility of our results.Article Citation - WoS: 7Citation - Scopus: 10Some New Results for Ψ - Hilfer Fractional Pantograph-Type Differential Equation Depending on Ψ - Riemann-Liouville Integral(Springernature, 2022) Bouriah, Soufyane; Benchohra, Mouffak; Karapinar, Erdal; Foukrach, DjamalThe aim of the present work is to study a large class of psi-Hilfer fractional differential equation of Pantograph-type depending on psi-Riemann-Liouville fractional integral operator associated with periodic-type fractional integral boundary conditions in a weighted space of continuous functions. We shall prove the existence and uniqueness results by means of Mawhin's coincidence degree theory. At the end, an illustrative example will be constructed to approve our findings.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: 17Citation - Scopus: 19Regularity Results for Fractional Diffusion Equations Involving Fractional Derivative With Mittag-Leffler Kernel(Wiley, 2020) Baleanu, Dumitru; Duc Le Thi Minh; Tuan Nguyen Huy; Ngoc Tran Bao; Nguyen Huy, Tuan; Tran Bao, Ngoc; Bao, Ngoc Tran; Le Thi Minh, Duc; Minh, Duc Le Thi; Huy, Tuan NguyenThis paper studies partial differential equation model with the new general fractional derivatives involving the kernels of the extended Mittag-Leffler type functions. An initial boundary value problem for the anomalous diffusion of fractional order is analyzed and considered. The fractional derivative with Mittag-Leffler kernel or also called Atangana and Baleanu fractional derivative in time is taken in the Caputo sense. We obtain results on the existence, uniqueness, and regularity of the solution.Article Citation - WoS: 28Citation - Scopus: 33Existence of Periodic Solutions, Global Attractivity and Oscillation of Impulsive Delay Population Model(Pergamon-elsevier Science Ltd, 2007) Alzabut, J. O.; Saker, S. H.In this paper we consider the nonlinear impulsive delay population model. The main objective is to systematically study the qualitative behavior of the model including existence of periodic solutions, global attractivity and oscillation. The main oscillation results are the results of the prevalence of the mature cells about the periodic solutions and the global attractivity results are the conditions for nonexistence of dynamical diseases on the population. (c) 2006 Elsevier Ltd. All rights reserved.