Browsing by Author "Mohammadi, Hakimeh"

Now showing 1 - 14 of 14

Citation Count: Baleanu, D...et al. (2016). A fractional derivative inclusion problem via an integral boundary condition. Journal of Computational Analysis and Applications, 21(3), 504-514.
A fractional derivative inclusion problem via an integral boundary condition
(Eudoxus Press, 2016) Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram
We 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.
Citation Count: Baleanu, Dumitru...at all (2020). "A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative", Advances in Difference Equations, Vol. 2020, No. 1.
A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative
(2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
We 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.
Citation Count: Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram (20209. "A mathematical theoretical study of a particular system of Caputo-Fabrizio fractional differential equations for the Rubella disease model", Advances in Difference Equations, Vol. 2020, No. 1.
A mathematical theoretical study of a particular system of Caputo-Fabrizio fractional differential equations for the Rubella disease model
(2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
In 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.
Citation Count: Baleanu, Dumitru...et al. (2021). "A novel modeling of boundary value problems on the glucose graph", Communications in Nonlinear Science and Numerical Simulation, Vol. 100.
A novel modeling of boundary value problems on the glucose graph
(2021) Baleanu, Dumitru; Etemad, Sina; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
In 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.
Citation Count: Baleanu, D.; Mohammadi, H.; Rezapour, S.,"Analysis of the Model of Hıv-1 Infection of Cd4 + T-Cell With A New Approach of Fractional Derivative",Advances in Difference Equations, Vol. 2020, No. 1, (2020).
Analysis of the Model of Hıv-1 Infection of Cd4 + T-Cell With A New Approach of Fractional Derivative
(Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
By 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.
Citation Count: Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram (2020). "Analysis of the model of HIV-1 infection of CD4(+) T-cell with a new approach of fractional derivative", Advances in Difference Equations, Vol. 2020, No. 1.
Analysis of the model of HIV-1 infection of CD4(+) T-cell with a new approach of fractional derivative
(2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
By 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.
Citation Count: Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram, "On a nonlinear fractional differential equation on partially ordered metric spaces", Advances In Difference Equations, (2013)
On A Nonlinear Fractional Differential Equation On Partially Ordered Metric Spaces
(Springer International Publishing AG, 2013) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
In this paper, by using a fixed point result on ordered metric spaces, we prove the existence and uniqueness of a solution of the nonlinear fractional differential equation (, ) via the periodic boundary condition , where and is a continuous increasing function and denotes the Caputo fractional derivative of order alpha. Also, we solve it by using the anti-periodic boundary conditions with and with and separately.
Citation Count: Baleanu, Dumitru...et al. (2020). "On modelling of epidemic childhood diseases with the Caputo-Fabrizio derivative by using the Laplace Adomian decomposition method", Alexandria Engineering Journal, Vol. 59, No. 5, pp. 3029-3039.
On modelling of epidemic childhood diseases with the Caputo-Fabrizio derivative by using the Laplace Adomian decomposition method
(2020) Baleanu, Dumitru; Aydogn, Seher Melike; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
We 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. © 2020
Citation Count: Aydoğan, Seher Melike...et al. (2020). "On the mathematical model of Rabies by using the fractional Caputo-Fabrizio derivative", Advances in Difference Equations, Vol. 2020, No. 1.
On the mathematical model of Rabies by using the fractional Caputo-Fabrizio derivative
(2020) Aydoğan, Seher Melike; Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
Using 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.
Citation Count: Baleanu, D.; Mohammadi, H.; Rezapour, Sh. "Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations", Abstract and Applied Analysis, (2012)
Positive Solutions of An Initial Value Problem for Nonlinear Fractional Differential Equations
(Hindawi Publishing Corporation, 2012) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problem D(0+)(alpha)u(t) + D(0+)(beta)u(t) = f(t, u(t)), u(0) = 0, 0 < t < 1, where 0 < beta < alpha < 1, D-0+(alpha) is the standard Riemann-Liouville differentiation and f : [0,1] x [0,infinity) -> [0,infinity) is continuous. By using some fixed-point results on cones, some existence and multiplicity results of positive solutions are obtained.
Citation Count: Baleanu, Dumitru...et al. (2013). "Some Existence Results For A Nonlinear Fractional Differential Equation On Partially Ordered Banach Spaces", Boundary Value Problems.
Some Existence Results For A Nonlinear Fractional Differential Equation On Partially Ordered Banach Spaces
(Springer Open, 2013) Baleanu, Dumitru; Agarwal, Ravi P.; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
By using fixed point results on cones, we study the existence and uniqueness of positive solutions for some nonlinear fractional differential equations via given boundary value problems. Examples are presented in order to illustrate the obtained results.
Citation Count: Baleanu, D., Rezapour, S., Mohammadi, H. (2013). Some existence results on nonlinear fractional differential equations. Philosophical Transactions Of The Royal Society A-Mathematical Physical And Engineering Sciences, 371(1990). http://dx.doi.org/10.1098/rsta.2012.0144
Some existence results on nonlinear fractional differential equations
(Royal Soc, 2013) Baleanu, Dumitru; Rezapour, Shahram; Mohammadi, Hakimeh
In this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundary-value problem D(alpha)u(t) = f(t, u(t)) with a Riemann-Liouville fractional derivative via the different boundary-value problems u(0) = u(T), and the three-point boundary condition u(0)= beta(1)u(eta) and u(T) = beta(2)u(eta), where T > 0, t is an element of I = [0, T], 0 < alpha < 1, 0 < eta < T, 0 < beta(1) < beta(2) < 1.
Citation Count: Baleanu, Dumitru...et al. (2013). "The Existence of Solutions For a Nonlinear Mixed Problem of Singular Fractional Differential Equations", Advances In Difference Equations.
The Existence of Solutions For a Nonlinear Mixed Problem of Singular Fractional Differential Equations
(Springer Open, 2013) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389
By 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.
Citation Count: Mohammadi, Hakimeh...et al. (2020). "Two sequential fractional hybrid differential inclusions", Advances in Difference Equations, Vol. 2020, No. 1.
Two sequential fractional hybrid differential inclusions
(2020) Mohammadi, Hakimeh; Rezapour, Shahram; Etemad, Sina; Baleanu, Dumitru; 56389
The 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.