Browsing by Author "Rezapour, Shahram"

Now showing 1 - 20 of 49

Citation - WoS: 4
Citation - Scopus: 6
A fractional derivative inclusion problem via an integral boundary condition
(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; Matematik
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 - WoS: 153
Citation - Scopus: 185
A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative
(Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389; Matematik
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 - WoS: 5
A fractional finite difference inclusion
(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; Matematik
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 - WoS: 239
Citation - Scopus: 253
A Hybrid Caputo Fractional Modeling for Thermostat With Hybrid Boundary Value Conditions
(Springeropen, 2020) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; 56389; Matematik
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.
A k-Dimensional System of Fractional Finite Difference Equations
(2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; 56389; Matematik
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 - WoS: 6
Citation - Scopus: 13
A k-Dimensional System of Fractional Finite Difference Equations
(Hindawi Ltd, 2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; 56389; Matematik
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 - WoS: 3
Citation - Scopus: 3
A k-Dimensional System of Fractional Neutral Functional Differential Equations with Bounded Delay
(Hindawi Ltd, 2014) Baleanu, Dumitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram; 56389; Matematik
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 - WoS: 83
Citation - Scopus: 100
A mathematical theoretical study of a particular system of Caputo-Fabrizio fractional differential equations for the Rubella disease model
(Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389; Matematik
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 - WoS: 113
Citation - Scopus: 128
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; Matematik
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 - WoS: 667
Citation - Scopus: 709
A New Study On the Mathematical Modelling of Human Liver With Caputo–Fabrizio Fractional Derivative
(Pergamon-elsevier Science Ltd, 2020) Baleanu, Dumitru; Jajarmi, Amin; Mohammadi, Hakimeh; Rezapour, Shahram; 56389; Matematik
In this research, we aim to propose a new fractional model for human liver involving Caputo-Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard-Lindelof approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives. (C) 2020 Elsevier Ltd. All rights reserved.
Citation - WoS: 108
Citation - Scopus: 111
A novel modeling of boundary value problems on the glucose graph
(Elsevier, 2021) Baleanu, Dumitru; Etemad, Sina; Mohammadi, Hakimeh; Rezapour, Shahram; 56389; Matematik
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. (c) 2021 Elsevier B.V. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 2
An increasing variables singular system of fractional q-differential equations via numerical calculations
(Springer, 2020) Samei, Mohammad Esmael; Baleanu, Dumitru; Rezapour, Shahram; 56389; Matematik
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 - WoS: 258
Citation - Scopus: 256
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; Matematik
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.
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; Matematik
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 - WoS: 132
Citation - Scopus: 141
Analyzing Transient Response of the Parallel Rcl Circuit By Using the Caputo–Fabrizio Fractional Derivative
(Springeropen, 2020) Alizadeh, Shahram; Baleanu, Dumitru; Rezapour, Shahram; 56389; Matematik
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 - WoS: 4
Citation - Scopus: 6
Application of some special operators on the analysis of a new generalized fractional Navier problem in the context of q-calculus
(Springer, 2021) Etemad, Sina; Ntouyas, Sotiris K.; Imran, Atika; Hussain, Azhar; Baleanu, Dumitru; Rezapour, Shahram; 56389; Matematik
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 - WoS: 22
Citation - Scopus: 24
Attractivity for a k-dimensional system of fractional functional differential equations and global attractivity for a k-dimensional system of nonlinear fractional differential equations
(Springeropen, 2014) Baleanu, Dumitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram; 56389; Matematik
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 - WoS: 12
Citation - Scopus: 11
Criteria for existence of solutions for a Liouville–Caputo boundary value problem via generalized Gronwall’s inequality
(Springer, 2021) Mohammadi, Hakimeh; Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; 56389; Matematik
In 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.
Citation - WoS: 22
Citation - Scopus: 22
Existence and Uniqueness of Solutions For Multi-Term Nonlinear Fractional Integro-Differential Equations
(Springeropen, 2013) Baleanu, Dumitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram; 56389; Matematik
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 - WoS: 5
Citation - Scopus: 8
On a Caputo conformable inclusion problem with mixed Riemann–Liouville conformable integro-derivative conditions
(Springer, 2020) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; 56389; Matematik
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 alpha-psi-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.