Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 4Citation - Scopus: 6A Fractional Derivative Inclusion Problem Via an Integral Boundary Condition(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; MatematikWe investigate the existence of solutions for the fractional differential inclusion (c)D(alpha)x(t) is an element of F(t, x(t)) (equipped with the boundary value problems x(0) = 0 and x(1) = integral(eta)(0) x(s)ds, where 0 < eta < 1, 1 < alpha <= 2, D-c(alpha) is the standard Caputo differentiation and F : [0, 1] x R -> 2(R) is a compact valued multifunction. An illustrative example is also discussed.Article Citation - WoS: 124Citation - Scopus: 140On Modelling of Epidemic Childhood Diseases With the Caputo-Fabrizio Derivative by Using the Laplace Adomian Decomposition Method(Elsevier, 2020) Aydogn, Seher Melike; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruWe present a fractional-order epidemic model for childhood diseases with the new fractional derivative approach proposed by Caputo and Fabrizio. By applying the Laplace Adomian decomposition method (LADM), we solve the problem and the solutions are presented as infinite series converging to the solution. We prove the existence, uniqueness, and stability of the solution by using the fixed point theory. Also, we provide some numerical results to illustrate the effectiveness of the new derivative. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.Article Citation - WoS: 15Citation - Scopus: 14Criteria for Existence of Solutions for a Liouville-Caputo Boundary Value Problem Via Generalized Gronwall's Inequality(Springer, 2021) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; Mohammadi, HakimehIn this research, we first investigate the existence of solutions for a new fractional boundary value problem in the Liouville-Caputo setting with mixed integro-derivative boundary conditions. To do this, Kuratowski's measure of noncompactness and Sadovskii's fixed point theorem are our tools to reach this aim. In the sequel, we discuss the continuous dependence of solutions on parameters by means of the generalized Gronwall inequality. Moreover, we consider an inclusion version of the given boundary problem in which we study its existence results by means of the endpoint theory. Finally, we prepare two simulative numerical examples to confirm the validity of the analytical findings.Article Citation - WoS: 117Citation - Scopus: 120A Novel Modeling of Boundary Value Problems on the Glucose Graph(Elsevier, 2021) Etemad, Sina; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruIn this article, with due attention to a new labeling method for vertices of arbitrary graphs, we investigate the existence results for a novel modeling of the fractional multi term boundary value problems on each edge of the graph representation of the Glucose molecule. In this direction, we consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of the Glucose molecule and then derive some existence results by applying two known fixed point theorems. Finally, we provide an example to illustrate the validity of our main result. (c) 2021 Elsevier B.V. All rights reserved.Article Analysis of the model of HIV-1 infection of CD4(+) T-cell with a new approach of fractional derivative(Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, ShahramBy using the fractional Caputo-Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.Article Citation - WoS: 85Citation - Scopus: 104A Mathematical Theoretical Study of a Particular System of Caputo-Fabrizio Fractional Differential Equations for the Rubella Disease Model(Springer, 2020) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruIn this paper, we study the rubella disease model with the Caputo-Fabrizio fractional derivative. The mathematical solution of the liver model is presented by a three-step Adams-Bashforth scheme. The existence and uniqueness of the solution are discussed by employing fixed point theory. Finally some numerical simulations are showed to underpin the effectiveness of the used derivative.Article Citation - WoS: 160Citation - Scopus: 194A Fractional Differential Equation Model for the Covid-19 Transmission by Using the Caputo-Fabrizio Derivative(Springer, 2020) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruWe present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.Article Citation - WoS: 29Citation - Scopus: 33Two Sequential Fractional Hybrid Differential Inclusions(Springer, 2020) Rezapour, Shahram; Etemad, Sina; Baleanu, Dumitru; Mohammadi, HakimehThe main objective of this paper is to concern with a new category of the sequential hybrid inclusion boundary value problem with three-point integro-derivative boundary conditions. In this direction, we employ various novel analytical techniques based on alpha-psi-contractive mappings, endpoints, and the fixed points of the product operators to obtain the main results. Finally, we provide two examples to illustrate our main results.Article Citation - WoS: 69Citation - Scopus: 74On the Mathematical Model of Rabies by Using the Fractional Caputo-Fabrizio Derivative(Springer, 2020) Aydogan, Seher Melike; Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, ShahramUsing the fractional Caputo-Fabrizio derivative, we investigate a new version of the mathematical model of Rabies disease. Using fixed point results, we prove the existence of a unique solution. We calculate the equilibrium points and check the stability of solutions. We solve the equation by combining the Laplace transform and Adomian decomposition method. In numerical results, we investigate the effect of coefficients on the number of infected groups. We also examine the effect of derivation orders on the behavior of functions and make a comparison between the results of the integer-order derivative and the Caputo and Caputo-Fabrizio fractional-order derivatives.Article Citation - WoS: 273Citation - Scopus: 268Analysis of the Model of Hiv-1 Infection of Cd4<sup>+</Sup> T-Cell With a New Approach of Fractional Derivative(Springer, 2020) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruBy using the fractional Caputo-Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.