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: 5Citation - Scopus: 6Application of Some Special Operators on the Analysis of a New Generalized Fractional Navier Problem in the Context of Q-Calculus(Springer, 2021) Ntouyas, Sotiris K.; Imran, Atika; Hussain, Azhar; Baleanu, Dumitru; Rezapour, Shahram; Etemad, SinaThe key objective of this study is determining several existence criteria for the sequential generalized fractional models of an elastic beam, fourth-order Navier equation in the context of quantum calculus (q-calculus). The required way to accomplish the desired goal is that we first explore an integral equation of fractional order w.r.t. q-RL-integrals. Then, for the existence of solutions, we utilize some fixed point and endpoint conditions with the aid of some new special operators belonging to operator subclasses, orbital alpha-admissible and alpha-psi-contractive operators and multivalued operators involving approximate endpoint criteria, which are constructed by using aforementioned integral equation. Furthermore, we design two examples to numerically analyze our results.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: 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: 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.Article Citation - WoS: 38Citation - Scopus: 42The Existence of Solutions for Some Fractional Finite Difference Equations Via Sum Boundary Conditions(Springer, 2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; Agarwal, Ravi P.In this manuscript we investigate the existence of the fractional finite difference equation (FFDE) Delta(mu)(mu-2)x(t) = g(t + mu - 1, x(t + mu - 1), Delta x(t + mu - 1)) via the boundary condition x(mu - 2) = 0 and the sum boundary condition x(mu + b + 1) = Sigma(alpha)(k=mu-1) x(k) for order 1 < mu <= 2, where g : N-mu-1(mu+b+1) x R x R -> R, alpha is an element of N-mu-1(mu+b), and t is an element of N-0(b+2). Along the same lines, we discuss the existence of the solutions for the following FFDE: Delta(mu)(mu-3)x(t) = g(t + mu - 2, x(t + mu - 2)) via the boundary conditions x(mu - 3) = 0 and x(mu + b + 1) = 0 and the sum boundary condition x(alpha) = Sigma(beta)(k=gamma)x(k) for order 2 < mu <= 3, where g : N-mu-2(mu+b+1) x R -> R, b is an element of N-0, t is an element of N-0(b+3), and alpha, beta,gamma N-mu-2(mu+b) with gamma < beta < alpha.Article Citation - WoS: 60Citation - Scopus: 65The Existence of Solutions for a Nonlinear Mixed Problem of Singular Fractional Differential Equations(Springer, 2013) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruBy using fixed point results on cones, we study the existence of solutions for the singular nonlinear fractional boundary value problem (c)D(alpha)u(t) = f(t, u(t), u'(t), (c)D(beta)u(t)), u(0) = au(1), u'(0) = b(c)D(beta)u(1), u ''(0) = u'''(0) = u((n-1))(0) = 0, where n >= 3 is an integer, alpha is an element of (n - 1, n), 0 < beta < 1, 0 < a < 1, 0 < b < Gamma (2 - beta), f is an L-q-Caratheodory function, q > 1/alpha-1 and f(t,x,y,z) may be singular at value 0 in one dimension of its space variables x, y, z. Here, D-c stands for the Caputo fractional derivative.Article Citation - WoS: 58Citation - Scopus: 64On Two Fractional Differential Inclusions(Springer international Publishing Ag, 2016) Hedayati, Vahid; Rezapour, Shahram; Al Qurashi, Maysaa' Mohamed; Baleanu, DumitruWe investigate in this manuscript the existence of solution for two fractional differential inclusions. At first we discuss the existence of solution of a class of fractional hybrid differential inclusions. To illustrate our results we present an illustrative example. We study the existence and dimension of the solution set for some fractional differential inclusions.Article Citation - WoS: 66Citation - Scopus: 74Two Fractional Derivative Inclusion Problems Via Integral Boundary Condition(Elsevier Science inc, 2015) Baleanu, Dumitru; Hedayati, Vahid; Rezapour, Shahram; Agarwal, Ravi P.; Moghaddam, Mehdi; Mohammadi, HakimehThe goal of the manuscript is to analyze the existence of solutions for the Caputo fractional differential inclusion (c)D(q)x(t) is an element of F(t,x(t), (c)D(beta)x(t)) with the boundary value conditions x(0) = 0 and x(1) + x'(1) = integral(eta)(0) x(s)ds, such that 0 < eta < 1, 1 < q <= 2, 0 < beta < 1 and q = beta > 1. Also, we investigate the existence of solutions for the Caputo fractional differential inclusion (c)D(q)x(t) is an element of F(t,x(t)) such that x(0) = a integral(nu)(0) x(s)ds and x(1) = b integral(eta)(0) x(s)ds, where 0 < nu, eta < 1, 1 < q <= 2 and a, b is an element of R. (C) 2014 Elsevier Inc. 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