Browsing by Author "Rezapour, Shahram"

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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.
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 - WoS: 267
Citation - Scopus: 264
Analysis of the Model of Hiv-1 Infection of Cd4⁺ T-Cell With a New Approach of Fractional Derivative
(Springer, 2020) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru; 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 - WoS: 132
Citation - Scopus: 141
Analyzing Transient Response of the Parallel Rcl Circuit by Using the Caputo-Fabrizio Fractional Derivative
(Springeropen, 2020) Baleanu, Dumitru; Rezapour, Shahram; Alizadeh, 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 - WoS: 5
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) Ntouyas, Sotiris K.; Imran, Atika; Hussain, Azhar; Baleanu, Dumitru; Rezapour, Shahram; Etemad, Sina; 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 - 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) Nazemi, Sayyedeh Zahra; Rezapour, Shahram; Baleanu, Dumitru; 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 - WoS: 13
Citation - Scopus: 12
Criteria 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, Hakimeh; 56389
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: 23
Existence and Uniqueness of Solutions for Multi-Term Nonlinear Fractional Integro-Differential Equations
(Springeropen, 2013) Nazemi, Sayyedeh Zahra; Rezapour, Shahram; Baleanu, Dumitru; 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 - WoS: 16
Citation - Scopus: 23
The Existence of Positive Solutions for a New Coupled System of Multiterm Singular Fractional Integrodifferential Boundary Value Problems
(Hindawi Ltd, 2013) Nazemi, Sayyedeh Zahra; Rezapour, Shahram; Baleanu, Dumitru; 56389
We discuss the existence of positive solutions for the coupled system of multiterm singular fractional integrodifferential boundary value problems D-0+(alpha) + f(1)(t), u(t), v(t), (phi(1)u)(t), (psi(1)v)(t), D(0+)(p)u(t), D(0+)(mu 1)v(t), D(0+)(mu 2)v(t), ... , D(0+)(mu m)v(t)) = 0, D(0+)(beta)v(t) + f(2)(t, u(t), v(t), (phi(2)u)(t), (psi(2)v)(t), D(0+)(q)v(t), D(0+)(v1)v(t), D(0+)(v2)v(t), ... , D(0+)(vm)v(t) = 0, u((1))(0) = 0 and v((i))(0) = 0 for all 0 <= i <= n - 2, [D(0+)(delta 1)u(t)](t=1) - 0 for 2 < delta(1) < n - 1 and alpha - delta(1) >= 1, [D(0+)(delta 2)u(t)](t=1) - 0 for 2 < delta(2) < n - 1 and beta - delta(1) >= 1 where n >= 4 n - 1 < alpha, beta < n, 0 < 1, 1 < mu(i,) nu(i) < 2 (i = 1, 2, ... , m), gamma(j,) lambda(j) : [0, 1] x [0, 1] -> (0, infinity) are continuous functions (j = 1, 2) and (phi(j)u)(t) = integral(t)(0) gamma(j)(t, s)u(s)ds, (psi(j)v)(t) = integral(t)(0) gamma(j)(t, s)v(s)ds. Here D is the standard Riemann-Liouville fractional derivative, f(j) (j = 1, 2) is a Caratheodory function, and f(j)(t, x, y, z, w, v, u(1), u(2), ... , u(m)) is singular at the value 0 of its variables.
Citation - WoS: 10
Citation - Scopus: 11
The Existence of Solution for a K-Dimensional System of Multiterm Fractional Integrodifferential Equations With Antiperiodic Boundary Value Problems
(Hindawi Publishing Corporation, 2014) Nazemi, Sayyedeh Zahra; Rezapour, Shahram; Baleanu, Dumitru; 56389
There are many published papers about fractional integrodifferential equations and system of fractional differential equations. The goal of this paper is to show that we can investigate more complicated ones by using an appropriate basic theory. In this way, we prove the existence and uniqueness of solution for k-dimensional system of multiterm fractional integrodifferential equations with antiperiodic boundary conditions by applying some standard fixed point results. An illustrative example is also presented.
Citation - WoS: 56
Citation - Scopus: 61
The Existence of Solutions for a Nonlinear Mixed Problem of Singular Fractional Differential Equations
(Springer, 2013) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru; 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 - WoS: 38
Citation - Scopus: 42
The Existence of Solutions for Some Fractional Finite Difference Equations Via Sum Boundary Conditions
(Springer, 2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; Agarwal, Ravi P.; 56389
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.
Citation - WoS: 66
Citation - Scopus: 74
The Extended Fractional Caputo-Fabrizio Derivative of Order 0 ≤ Σ < 1 on Cr[0,1] and the Existence of Solutions for Two Higher-Order Series-Type Differential Equations
(Springeropen, 2018) Mousalou, Asef; Rezapour, Shahram; Baleanu, Dumitru; 56389
We extend the fractional Caputo-Fabrizio derivative of order 0 <= sigma < 1 on C-R[0,1] and investigate two higher-order series-type fractional differential equations involving the extended derivation. Also, we provide an example to illustrate one of the main results.
Citation - WoS: 4
Citation - Scopus: 6
A Fractional Derivative Inclusion Problem Via an Integral Boundary Condition
(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; 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: 157
Citation - Scopus: 191
A Fractional Differential Equation Model for the Covid-19 Transmission by Using the Caputo-Fabrizio Derivative
(Springer, 2020) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru; 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 - WoS: 5
A Fractional Finite Difference Inclusion
(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; 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: 241
Citation - Scopus: 257
A Hybrid Caputo Fractional Modeling for Thermostat With Hybrid Boundary Value Conditions
(Springeropen, 2020) Etemad, Sina; Rezapour, Shahram; Baleanu, Dumitru; 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.
Citation - WoS: 2
Citation - Scopus: 2
An Increasing Variables Singular System of Fractional Q-Differential Equations Via Numerical Calculations
(Springer, 2020) Baleanu, Dumitru; Rezapour, Shahram; Samei, Mohammad Esmael; 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 - WoS: 6
Citation - Scopus: 13
A K-Dimensional System of Fractional Finite Difference Equations
(Hindawi Ltd, 2014) Rezapour, Shahram; Salehi, Saeid; Baleanu, Dumitru; 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 - WoS: 3
Citation - Scopus: 4
A K-Dimensional System of Fractional Neutral Functional Differential Equations With Bounded Delay
(Hindawi Ltd, 2014) Nazemi, Sayyedeh Zahra; Rezapour, Shahram; Baleanu, Dumitru; 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..