Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 5Citation - Scopus: 7On Some Self-Adjoint Fractional Finite Difference Equations(Eudoxus Press, Llc, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; MatematikRecently, 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.Article Citation - WoS: 4Citation - Scopus: 6A Fractional Derivative Inclusion Problem Via an Integral Boundary Condition(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; MatematikWe 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.Article Citation - WoS: 5A Fractional Finite Difference Inclusion(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; MatematikIn 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.Article Citation - WoS: 103Citation - Scopus: 107Some Novel Mathematical Analysis on the Fractal-Fractional Model of the Ah1n1/09 Virus and Its Generalized Caputo-Type Version(Pergamon-elsevier Science Ltd, 2022) Avci, Ibrahim; Kumar, Pushpendra; Baleanu, Dumitru; Rezapour, Shahram; Etemad, SinaIn this paper, we formulate a new model of a particular type of influenza virus called AH1N1/09 in the framework of the four classes consisting of susceptible, exposed, infectious and recovered people. For the first time, we here investigate this model with the help of the advanced operators entitled the fractal-fractional operators with two fractal and fractional orders via the power law type kernels. The existence of solution for the mentioned fractal-fractional model of AH1N1/09 is studied by some special mappings such as ?-psi-contractions and ?-admissibles. The Leray-Schauder theorem is also applied for this aim. After investigating the stability criteria in four versions, to approximate the desired numerical solutions, we implement Adams-Bashforth (AB) scheme and simulate the graphs for different data on the fractal and fractional orders. Lastly, we convert our fractal-fractional AH1N1/09 model into a fractional model via the generalized Liouville-Caputo-type (GLC-type) operators and then, we simulate new graphs caused by the new numerical scheme called Kumar-Erturk method.Article Citation - WoS: 67Citation - Scopus: 75The 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, DumitruWe 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.Article Citation - WoS: 4Citation - Scopus: 4On Solutions of Fractional Multi-Term Sequential Problems Via Some Special Categories of Functions and (aep)-Property(Springer, 2021) Iqbal, Muhammad Qamar; Hussain, Azhar; Etemad, Sina; Rezapour, Shahram; Baleanu, DumitruThe main intention of this article is that new techniques of existence theory are used to derive some required criteria pertinent to a given fractional multi-term problem and its inclusion version. In such an approach, we do our research on a fractional integral equation corresponding to the mentioned BVPs. In more precise words, by virtue of this integral equation, we construct new operators which belong to a special category of functions named alpha-admissible and alpha-psi-contraction maps coupled with operators having (AEP)-property. Next, by considering some new properties on the existing Banach space having properties (B) and (C-alpha), our argument for ensuring the existence of solutions is completed. In addition, we also add two simulative examples to review our findings by a numerical view.Article Citation - WoS: 124Citation - Scopus: 140On 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, DumitruWe 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.Article Citation - WoS: 103Citation - Scopus: 114On Coupled Systems of Time-Fractional Differential Problems by Using a New Fractional Derivative(Hindawi Ltd, 2016) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; Alsaedi, AhmedThe existence of solutions for a coupled system of time-fractional differential equations including continuous functions and the Caputo-Fabrizio fractional derivative is examined. After that we investigated a coupled system of time-fractional differential inclusions including compact-and convex-valued L-1-Caratheodory multifunctions and the Caputo-Fabrizio fractional derivative.Article Citation - WoS: 8Citation - Scopus: 10On a Caputo Conformable Inclusion Problem With Mixed Riemann-Liouville Conformable Integro-Derivative Conditions(Springer, 2020) Etemad, Sina; Rezapour, Shahram; Baleanu, DumitruWe 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.Article Citation - WoS: 15Citation - Scopus: 14Criteria 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, HakimehIn 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.