Browsing by Author "Rezapour, Shahram"

Now showing 1 - 20 of 47

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, D., Rezapour, S., Salehi, S. (2016). A fractional finite difference inclusion. Journal of Computational Analysis and Applications, 20(5), 834-842.
A fractional finite difference inclusion
(Eudoxus Press, 2016) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid
In this manuscript we investigated the fractional finite difference inclusion Delta(mu)(mu-2) x(t) is an element of F(t, x(t), Delta x(t)) via the boundary conditions Delta x(b + mu) = A and x(mu - 2) = B, where 1 <= 2, A,B is an element of R and F :N-mu-2(b+mu+2) x R -> 2(R) is a compact valued multifunction.
Citation Count: Baleanu, Dimitru; Etemad, S.; Rezapour, S. "A Hybrid Caputo Fractional Modeling for Thermostat With Hybrid Boundary Value Conditions", Boundary Value Problems, Vol. 2020, No.1, (2020).
A Hybrid Caputo Fractional Modeling for Thermostat With Hybrid Boundary Value Conditions
(Springer, 2020) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; 56389
We provide an extension for the second-order differential equation of a thermostat model to the fractional hybrid equation and inclusion versions. We consider boundary value conditions of this problem in the form of the hybrid conditions. To prove the existence of solutions for our hybrid fractional thermostat equation and inclusion versions, we apply the well-known Dhage fixed point theorems for single-valued and set-valued maps. Finally, we give two examples to illustrate our main results. © 2020, The Author(s).
Citation Count: Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid (2014). "A k-Dimensional System of Fractional Finite Difference Equations", Abstract and Applied Analysis.
A k-Dimensional System of Fractional Finite Difference Equations
(2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; 56389
We investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.
Citation Count: Baleanu, Dimitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram, "A k-Dimensional System of Fractional Neutral Functional Differential Equations with Bounded Delay", Abstract and Applied Analysis, (2014).
A k-Dimensional System of Fractional Neutral Functional Differential Equations with Bounded Delay
(Hindawi LTD, 2014) Baleanu, Dumitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram; 56389
In 2010, Agarwal et al. studied the existence of a one-dimensional fractional neutral functional differential equation. In this paper, we study an initial value problem for a class of k-dimensional systems of fractional neutral functional differential equations by using Krasnoselskii's fixed point theorem. In fact, our main result generalizes their main result in a sense..
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; Mousalou, Asef; Rezapour, Shahram (2017). A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo-Fabrizio derivative, Advances in Difference Equations.
A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo-Fabrizio derivative
(Springer International Publishing AG, 2017) Baleanu, Dumitru; Mousalou, Asef; Rezapour, Shahram; 56389
We present a new method to investigate some fractional integro-differential equations involving the Caputo-Fabrizio derivation and we prove the existence of approximate solutions for these problems. We provide three examples to illustrate our main results. By checking those, one gets the possibility of using some discontinuous mappings as coefficients in the fractional integro-differential equations.
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: Samei, Mohammad Esmael; Baleanu, Dumitru; Rezapour, Shahram (2020). "An increasing variables singular system of fractional q-differential equations via numerical calculations", Advances in Difference Equations, Vol. 2020, No. 1.
An increasing variables singular system of fractional q-differential equations via numerical calculations
(2020) Samei, Mohammad Esmael; Baleanu, Dumitru; Rezapour, Shahram; 56389
We investigate the existence of solutions for an increasing variables singular m-dimensional system of fractional q-differential equations on a time scale. In this singular system, the first equation has two variables and the number of variables increases permanently. By using some fixed point results, we study the singular system under some different conditions. Also, we provide two examples involving practical algorithms, numerical tables, and some figures to illustrate our main results.
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: Alizadeh, S.; Baleanu, D.; Rezapour, S.,"Analyzing Transient Response of the Parallel Rcl Circuit By Using the Caputo–Fabrizio Fractional Derivative",Advances in Difference Equations, Vol. 2020, No. 1, (2020).
Analyzing Transient Response of the Parallel Rcl Circuit By Using the Caputo–Fabrizio Fractional Derivative
(Springer, 2020) Alizadeh, Shahram; Baleanu, Dumitru; Rezapour, Shahram; 56389
In this paper, the transient response of the parallel RCL circuit with Caputo–Fabrizio derivative is solved by Laplace transforms. Also, the graphs of the obtained solutions for the different orders of the fractional derivatives are compared with each other and with the usual solutions. Finally, they are compared with practical and laboratory results.
Citation Count: Etemad, Sina...et al. (2021). "Application of some special operators on the analysis of a new generalized fractional Navier problem in the context of q-calculus", Advances in Difference Equations, Vol. 2021, No. 1.
Application of some special operators on the analysis of a new generalized fractional Navier problem in the context of q-calculus
(2021) Etemad, Sina; Ntouyas, Sotiris K.; Imran, Atika; Hussain, Azhar; Baleanu, Dumitru; Rezapour, Shahram; 56389
The 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.
Citation Count: Baleanu, Dumitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram (2014). "Attractivity for a k-dimensional system of fractional functional differential equations and global attractivity for a k-dimensional system of nonlinear fractional differential equations", Journal of Inequalities and Applications.
Attractivity for a k-dimensional system of fractional functional differential equations and global attractivity for a k-dimensional system of nonlinear fractional differential equations
(2014) Baleanu, Dumitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram; 56389
In this paper, we present some results for the attractivity of solutions for a k-dimensional system of fractional functional differential equations involving the Caputo fractional derivative by using the classical Schauder's fixed-point theorem. Also, the global attractivity of solutions for a k-dimensional system of fractional differential equations involving Riemann-Liouville fractional derivative are obtained by using Krasnoselskii's fixed-point theorem. We give two examples to illustrate our main results.
Citation Count: Baleanu, Dimitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram, "Existence and Uniqueness of Solutions For Multi-Term Nonlinear Fractional Integro-Differential Equations", Advances In Difference Equations, (2013).
Existence and Uniqueness of Solutions For Multi-Term Nonlinear Fractional Integro-Differential Equations
(Springer Open, 2013) Baleanu, Dumitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram; 56389
In this manuscript, by using the fixed point theorems, the existence and the uniqueness of solutions for multi-term nonlinear fractional integro-differential equations are reported. Two examples are presented to illustrate our results.
Citation Count: Cao, Yan...et al. (2021). "Extracting novel categories of analytical wave solutions to a nonlinear Schrödinger equation of unstable type", Results in Physics, Vol. 31.
Extracting novel categories of analytical wave solutions to a nonlinear Schrödinger equation of unstable type
(2021) Cao, Yan; Dhahad, Hayder A.; Jarad, Fahd; Sharma, Kamal; Rajhi, Ali A.; El-Shafay, A.S.; Rashidi, Shima; Rezapour, Shahram; Najati, S.A.; Aly, Ayman A; Alghtani, Abdulaziz H.; Riaz, Muhammad Bilal; 234808
Solving partial differential equations has always been one of the significant tools in mathematics for modeling applied phenomena. In this paper, using an efficient analytical technique, exact solutions for the unstable Schrödinger equation are constructed. This type of the Schrödinger equation describes the disturbance of time period in slightly stable and unstable media and manages the instabilities of lossless symmetric two stream plasma and two layer baroclinic. The basis of this method is the generalization of some commonly used methods in the literature. To better demonstrate the results, we perform many numerical simulations corresponding to the solutions. All these solutions are new achievements for this form of the equation that have not been acquired in previous research. As one of the strengths of the article, it can be pointed out that not only is the method very straightforward, but also can be used without the common computational complexities observed in known analytical methods. In addition, during the use of the method, an analytical solution is obtained in terms of familiar elementary functions, which will make their use in practical applications very convenient. On the other hand, the utilized methodology empowers us to handle other types of well-known models. All numerical results and simulations in this article have been obtained using computational packages in Wolfram Mathematica. © 2021 The Authors
Citation Count: Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram (2020). "On a Caputo conformable inclusion problem with mixed Riemann–Liouville conformable integro-derivative conditions", Advances in Difference Equations, Vol. 2020, No. 1.
On a Caputo conformable inclusion problem with mixed Riemann–Liouville conformable integro-derivative conditions
(2020) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; 56389
We discuss some existence criteria for a new category of the Caputo conformable differential inclusion furnished with four-point mixed Riemann–Liouville conformable integro-derivative boundary conditions. In this way, we employ some analytical techniques on α-ψ-contractive mappings and operators having the approximate endpoint property to reach desired theoretical results. Finally, we provide an example to illustrate our last main result. © 2020, The Author(s).
Citation Count: Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram (2020). "On a fractional hybrid multi-term integro-differential inclusion with four-point sum and integral boundary conditions", Advances in Difference Equations, Vol. 2020, No. 1.
On a fractional hybrid multi-term integro-differential inclusion with four-point sum and integral boundary conditions
(2020) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; 56389
We investigate the existence of solutions for a fractional hybrid multi-term integro-differential inclusion with four-point sum and integral boundary value conditions. By using Dhage's fixed point results, we prove our main existence result. Finally, we give an example to illustrate our main result.
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.