Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Population Dynamic Caused by War Involvement via Fractional Derivative on Time Scales(Inderscience Publishers, 2019) Baleanu, Dumitru; Agheli, Bahram; Neamaty, Abdolali; Nategh, MehdiArticle Citation - WoS: 2Citation - Scopus: 2Analysis of the New Technique To Solution of Fractional Wave- and Heat-Like Equation(Jagiellonian Univ Press, 2017) Agheli, Bahram; Darzi, Rahmat; Baleanu, DumitruWe have applied the new approach of homotopic perturbation method (NHPM) for wave- and heat-like equation featuring time-fractional derivative. A combination of NHPM and multiple fractional power series form has been used the first time to present analytical solution. In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given. All computations were done using Mathematica.Article Citation - WoS: 7Citation - Scopus: 9Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators(Mdpi, 2020) Darzi, Rahmat; Agheli, Bahram; Baleanu, DumitruA new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense.Article Citation - WoS: 6Citation - Scopus: 7A Reliable Mixed Method for Singular Integro-Differential Equations of Non-Integer Order(Edp Sciences S A, 2018) Darzi, Rahmat; Agheli, Ahram; Baleanu, Dumitru; Agheli, BahramIt is our goal in this article to apply a method which is based on the assumption that combines two methods of conjugating collocation and multiple shooting method. The proposed method can be used to find the numerical solution of singular fractional integro-differential boundary value problems (SFIBVPs) D-upsilon y(t) + eta integral(t)(0) (t - s)(zeta-1) y(s) ds = g(t), 1 < upsilon <= 2, 0 < zeta < 1, eta is an element of R, where D-upsilon denotes the Caputo derivative of order upsilon. Meanwhile, in a separate section the existence and uniqueness of this method is also discussed. Two examples are presented to illustrate the application and further understanding of the methods.Article Citation - WoS: 17Citation - Scopus: 18New Study of Weakly Singular Kernel Fractional Fourth-Order Partial Integro-Differential Equations Based on the Optimum Q-Homotopic Analysis Method(Elsevier, 2017) Darzi, Rahmat; Agheli, Bahram; Baleanu, DumitruIn this study, the optimum q-homotopic analysis method is employed to solve fourth order partial integro-differential equations with high-order non-integer derivatives. Several specific and clear examples are also given to illustrate the simplicity and capacity of the proposed approach. All of the computations were performed using Mathematica. (C) 2017 Elsevier B.V. All rights reserved.Article Citation - WoS: 2Citation - Scopus: 2Population Dynamic Caused by War Involvement Via Fractional Derivative on Time Scales(inderscience Enterprises Ltd, 2019) Baleanu, Dumitru; Neamaty, Abdolali; Agheli, Bahram; Nategh, MehdiThis work suggests a model for a population dynamic caused by an enemy attack to a domain of residential areas. With the help of a local non-integer order rate of change and a new structure induced on the real line, we derive a spatial discrete diffusion equation of fractional order. Then making use of the d'Alembert's change of variable we obtain a time scale which is made of union of disjoint compact intervals. These considerations lead us to a non-homogeneous second order nonlinear differential equation. The existence of a positive solution is discussed and through a numerical example the theory is illustrated.Article Citation - WoS: 11Citation - Scopus: 13An Optimal Method for Approximating the Delay Differential Equations of Noninteger Order(Springer, 2018) Agheli, Bahram; Darzi, Rahmat; Baleanu, DumitruThe main purpose of this paper is to use a method with a free parameter, named the optimal asymptotic homotopy method (OHAM), in order to obtain the solution of delay differential equations, delay partial differential equations, and a system of coupled delay equations featuring fractional derivative. This method is preferable to others since it has faster convergence toward homotopy perturbation method, and the convergence rate can be set as a controlled area. Various examples are given to better understand the use of this method. The approximate solutions are compared with exact solutions as well.Article Citation - WoS: 49Citation - Scopus: 51Fractional Advection Differential Equation Within Caputo and Caputo-Fabrizio Derivatives(Sage Publications Ltd, 2016) Agheli, Bahram; Al Qurashi, Maysaa Mohamed; Baleanu, DumitruIn this research, we applied the variational homotopic perturbation method and q-homotopic analysis method to find a solution of the advection partial differential equation featuring time-fractional Caputo derivative and time-fractional Caputo-Fabrizio derivative. A detailed comparison of the obtained results was reported. All computations were done using Mathematica.