Browsing by Author "Rezapour, Shahram"

Now showing 1 - 20 of 49

Citation - WoS: 142
Citation - Scopus: 161
On the Existence of Solutions for Some Infinite Coefficient-Symmetric Caputo-Fabrizio Fractional Integro-Differential Equations
(Springeropen, 2017) Mousalou, Asef; Rezapour, Shahram; Baleanu, Dumitru
By mixing the idea of 2-arrays, continued fractions, and Caputo-Fabrizio fractional derivative, we introduce a new operator entitled the infinite coefficient-symmetric Caputo-Fabrizio fractional derivative. We investigate the approximate solutions for two infinite coefficient-symmetric Caputo-Fabrizio fractional integro-differential problems. Finally, we analyze two examples to confirm our main 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
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: 29
Citation - Scopus: 31
On a Time-Fractional Integrodifferential Equation Via Three-Point Boundary Value Conditions
(Hindawi Ltd, 2015) Rezapour, Shahram; Etemad, Sina; Alsaedi, Ahmed; Baleanu, Dumitru
The existence and the uniqueness theorems play a crucial role prior to finding the numerical solutions of the fractional differential equations describing the models corresponding to the real world applications. In this paper, we study the existence of solutions for a time-fractional integrodifferential equation via three-point boundary value conditions.
Citation - WoS: 5
Citation - Scopus: 7
On Some Self-Adjoint Fractional Finite Difference Equations
(Eudoxus Press, Llc, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; Matematik
Recently, the existence of solution for the fractional self-adjoint equation Delta(nu)(nu-1) (p Delta y)(t) = h(t) for order 0 < nu <= 1 was reported in [9]. In this paper, we investigated the self-adjoint fractional finite difference equation Delta(nu)(nu-2)(p Delta u(t) = j(t,p(t+nu - 2)) via the boundary conditions y(nu - 2) = 0 , such that Delta y(nu - 2) = 0 and Delta y(nu+b) = 0. Also, we analyzed the self-adjoing fractional finite difference equation Delta(nu()(nu-2)p Delta(2)y)(t) = j(t,[(t+nu - 2)Delta(2)y(t+nu-3)) via the boundary conditions y(nu - 2) = 0, Delta y(nu - 2) = 0, Delta(2)y(nu - 2) = 0 and Delta 2y(nu+b) = 0. Finally, we conclude a result about the existence of solution for the general equation Delta(nu()(nu-2)p Delta(m)y)(t) = h(t,p(t+nu - m - 1)Delta(m)y(t+nu - m - 1)) via the boundary conditions y(nu - 2) = Delta y(nu - 2) = Delta(2)y(nu - 2) = center dot center dot center dot Delta(m)y(nu+b) = 0 for oder 1 < nu <= 2.
Citation - WoS: 160
Citation - Scopus: 164
On High Order Fractional Integro-Differential Equations Including the Caputo-Fabrizio Derivative
(Springeropen, 2018) Baleanu, Dumitru; Mousalou, Asef; Rezapour, Shahram; Aydogan, Melike S.
By using the fractional Caputo-Fabrizio derivative, we introduce two types new high order derivations called CFD and DCF. Also, we study the existence of solutions for two such type high order fractional integro-differential equations. We illustrate our results by providing two examples.
Citation - WoS: 8
Citation - Scopus: 10
On a Fractional Hybrid Multi-Term Integro-Differential Inclusion With Four-Point Sum and Integral Boundary Conditions
(Springer, 2020) Etemad, Sina; Rezapour, Shahram; Baleanu, Dumitru
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 - WoS: 118
Citation - Scopus: 132
A New Method for Investigating Approximate Solutions of Some Fractional Integro-Differential Equations Involving the Caputo-Fabrizio Derivative
(Springer international Publishing Ag, 2017) Mousalou, Asef; Rezapour, Shahram; Baleanu, Dumitru
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: 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
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: 115
Citation - Scopus: 119
A Novel Modeling of Boundary Value Problems on the Glucose Graph
(Elsevier, 2021) Etemad, Sina; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
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: 215
Citation - Scopus: 228
Some Existence Results on Nonlinear Fractional Differential Equations
(Royal Soc, 2013) Rezapour, Shahram; Mohammadi, Hakimeh; Baleanu, Dumitru
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 - WoS: 60
Citation - Scopus: 64
On the Existence of Solutions of a Three Steps Crisis Integro-Differential Equation
(Springer international Publishing Ag, 2018) Ghafarnezhad, Khadijeh; Rezapour, Shahram; Shabibi, Mehdi; Baleanu, Dumitru
There are many natural phenomena including a crisis (such as a spate or contest) which could be described in three steps. We investigate the existence of solutions for a three step crisis integro-differential equation. We suppose that the second step is a point-wise defined singular fractional differential equation.
Citation - WoS: 58
Citation - Scopus: 64
On Two Fractional Differential Inclusions
(Springer international Publishing Ag, 2016) Hedayati, Vahid; Rezapour, Shahram; Al Qurashi, Maysaa' Mohamed; Baleanu, Dumitru
We 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.
Citation - WoS: 120
Citation - Scopus: 137
On Modelling of Epidemic Childhood Diseases With the Caputo-Fabrizio Derivative by Using the Laplace Adomian Decomposition Method
(Elsevier, 2020) Aydogn, Seher Melike; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
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. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Citation - WoS: 711
Citation - Scopus: 755
A New Study on the Mathematical Modelling of Human Liver With Caputo-Fabrizio Fractional Derivative
(Pergamon-elsevier Science Ltd, 2020) Jajarmi, Amin; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
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: 84
Citation - Scopus: 103
A Mathematical Theoretical Study of a Particular System of Caputo-Fabrizio Fractional Differential Equations for the Rubella Disease Model
(Springer, 2020) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
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: 94
Citation - Scopus: 102
On Approximate Solutions for Two Higher-Order Caputo-Fabrizio Fractional Integro-Differential Equations
(Springeropen, 2017) Baleanu, Dumitru; Mousalou, Asef; Rezapour, Shahram; Aydogan, S. Melike
We investigate the existence of solutions for two high-order fractional differential equations including the Caputo-Fabrizio derivative. In this way, we introduce some new tools for obtaining solutions for the high-order equations. Also, we discuss two illustrative examples to confirm the reported results. In this way one gets the possibility of utilizing some continuous or discontinuous mappings as coefficients in the fractional differential equations of higher order.
Citation - WoS: 52
Citation - Scopus: 57
On a Nonlinear Fractional Differential Equation on Partially Ordered Metric Spaces
(Springer international Publishing Ag, 2013) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
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 - WoS: 270
Citation - Scopus: 265
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
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.
The extended fractional Caputo-Fabrizio derivative of order 0 <= sigma < 1 on C-R[0,1] and the existence of solutions for two higher-order series-type differential equations
(Springer Open, 2018) Baleanu, Dumitru; Mousalou, Asef; Rezapour, Shahram
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: 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
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..