Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 11Fractional Modeling of Viscous Fluid Over a Moveable Inclined Plate Subject To Exponential Heating With Singular and Non-Singular Kernels(Mdpi, 2022) Riaz, Muhammad Bilal; Rehman, Wajeeha; Awrejcewicz, Jan; Baleanu, Dumitru; Rehman, Aziz UrIn this paper, a new approach to investigating the unsteady natural convection flow of viscous fluid over a moveable inclined plate with exponential heating is carried out. The mathematical modeling is based on fractional treatment of the governing equation subject to the temperature, velocity and concentration field. Innovative definitions of time fractional operators with singular and non-singular kernels have been working on the developed constitutive mass, energy and momentum equations. The fractionalized analytical solutions based on special functions are obtained by using Laplace transform method to tackle the non-dimensional partial differential equations for velocity, mass and energy. Our results propose that by increasing the value of the Schimdth number and Prandtl number the concentration and temperature profiles decreased, respectively. The presence of a Prandtl number increases the thermal conductivity and reflects the control of thickness of momentum. The experimental results for flow features are shown in graphs over a limited period of time for various parameters. Furthermore, some special cases for the movement of the plate are also studied and results are demonstrated graphically via Mathcad-15 software.Article Citation - Scopus: 1Analytical and Numerical Solutions for Time-Fractional New Coupled Mkdv Equation Arising in Interaction of Two Long Waves(Asia Pacific Academic, 2019) Şenol, M.; Kurt, A.; Baleanu, D.; Tasbozan, O.The aim of this paper is to present new exact solution sets of nonlinear conformable time-fractional new coupled mKdV equations which arise in interaction of two long waves with different dispersion relations by means of sub-equation method. In addition, we also propose an analytical-approximate method namely residual power series method (RPSM) for the system. The fractional derivatives have been explained in newly defined conformable type, during the solution procedure. The exact solutions of the system obtained by the sub-equation method have been compared to approximate solutions derived by RPSM. The results showed that both methods are robust, dependable, easy to apply and a good alternative for seeking solutions of fractional partial differential equations. © 2019 Asia Pacific Journal of Mathematics.Article Citation - Scopus: 1Adapting Integral Transforms To Create Solitary Solutions for Partial Differential Equations Via a New Approach(New York Business Global Llc, 2023) Baleanu, Dumitru; Saadeh, Rania; Qazza, Ahmad; Burqan, AliaaIn this article, a new effective technique is implemented to solve families of nonlinear partial differential equations (NLPDEs). The proposed method combines the double ARA-Sumudu transform with the numerical iterative method to get the exact solutions of NLPDEs. The suc-cessive iterative method was used to find the solution of nonlinear terms of these equations. In order to show the efficiency and applicability of the presented method, some physical applications are analyzed and illustrated, and to defend our results, some numerical examples and figures are discussed.Article Citation - WoS: 2Citation - Scopus: 3Conformable Differential Operators for Meromorphically Multivalent Functions(de Gruyter Poland Sp Z O O, 2021) Baleanu, Dumitru; Jahangiri, Jay M.; Ibrahim, Rabha W.We define a conformable diff-integral operator for a class of meromorphically multivalent functions. We show that this conformable operator adheres to the semigroup property. We then use the subordination properties to prove inclusion conditions, sufficienrt inclusion conditions and convolution properties for this class of conformable operators.Article Citation - WoS: 28Citation - Scopus: 27Competitive Numerical Analysis for Stochastic Hiv/Aids Epidemic Model in a Two-Sex Population(inst Engineering Technology-iet, 2019) Rafiq, Muhammad; Baleanu, Dumitru; Shoaib Arif, Muhammad; Naveed, Muhammad; Ashraf, Kaleem; Raza, Ali; Arif, Muhammad ShoaibThis study is an attempt to explain a reliable numerical analysis of a stochastic HIV/AIDS model in a two-sex population considering counselling and antiretroviral therapy (ART). The authors are comparing the solutions of the stochastic and deterministic HIV/AIDS epidemic model. Here, an endeavour has been made to explain the stochastic HIV/AIDS epidemic model is comparatively more pragmatic in contrast with the deterministic HIV/AIDS epidemic model. The effect of threshold number H* holds on the stochastic HIV/AIDS epidemic model. If H* < 1 then condition helps us to control disease in a two-sex human population while H* > 1 explains the persistence of disease in the two-sex human population. Lamentably, numerical methods such as Euler-Maruyama, stochastic Euler, and stochastic Runge-Kutta do not work for large time step sizes. The recommended structure preserving framework of the stochastic non-standard finite difference (SNSFD) scheme conserve all vital characteristics such as positivity, boundedness, and dynamical consistency defined by Mickens. The effectiveness of counselling and ART may control HIV/AIDS in a two-sex population.Article Citation - WoS: 17Citation - Scopus: 19Competitive Analysis for Stochastic Influenza Model With Constant Vaccination Strategy(inst Engineering Technology-iet, 2019) Raza, Ali; Rafiq, Muhammad; Arif, Muhammad Shoaib; Ali, Muhammad Asghar; Baleanu, DumitruThis manuscript discusses a competitive analysis of stochastic influenza model with constant vaccination strategy. The stochastic influenza model is comparatively more pragmatic versus the deterministic influenza model. The effect of influenza generation number holds in the stochastic model. If the value of this number is less than one, this situation will help us to control the disease in a population. A greater than one value of this threshold number shows the persistence of disease to become endemic. The proposed structure for the stochastic influenza model as stochastic non-standard finite difference scheme conserve all vital characteristics like positivity, boundedness and dynamical consistency defined by Mickens.Article Citation - WoS: 19Citation - Scopus: 25Analysis for Fractional-Order Predator-Prey Model With Uncertainty(inst Engineering Technology-iet, 2019) Baleanu, Dumitru; Thangapandi, Kalidas; Perera, Shyam Sanjeewa Nishantha; Narayanamoorthy, SamayanHere, the authors analyse the fractional-order predator-prey model with uncertainty, due to the vast applications in various ecological systems. The most of the ecological model do not have exact analytic solution, so they proposed a numerical technique for an approximate solution. In the proposed method, they have implemented the higher order term into the fractional Euler method to enhance the precise solution. Further, the present attempt is aimed to discuss the solutions of the FPPM with uncertainty (fuzzy) initial conditions. The initial conditions of the predator-prey model were taken as fuzzy initial conditions due to the fact that the ecological model highly depends on uncertain parameters such as growth/decay rate, climatic conditions, and chemical reactions. Finally, the numerical example manifest that the proposed method is authentic, applicable, easy to use from a computational viewpoint and the acquired outcomes are balanced with the existing method (HPM), which shows the efficiency of the proposed method.Article Citation - Scopus: 5Criterion of the Approximate Controllability of a Class of Degenerate Distributed Systems With the Riemann- Derivative(M. K. Ammosov North-Eastern Federal University, 2019) Baleanu, D.; Taş, K.; Fedorov, V.E.; Gordievskikh, D.M.The issues of approximate controllability in fixed time and in free time of a class of distributed control systems whose dynamics are described by linear differential equations of fractional order in reflexive Banach spaces are investigated. It is assumed that the operator at the fractional Riemann-Liouville derivative has a non-trivial kernel, i. e., the equation is degenerate, and the pair of operators in the equation generates an analytic in a sector resolving family of operators of the corresponding homogeneous equation. The initial state of the control system is set by the Showalter-Sidorov type conditions. To obtain a criterion for the approximate controllability, the system is reduced to a set of two subsystems, one of which has a trivial form and the another is solved with respect to the fractional derivative. The equivalence of the approximate controllability of the system and of the approximate controllability of its two mentioned subsystems is proved. A criterion of the approximate controllability of the system is obtained in terms of the operators from the equation. The general results are used to find a criterion for the approximate controllability for a distributed control system, whose dynamics is described by the linearized quasistationary system of the phase field equations of a fractional order in time, as well as degenerate systems of the class under consideration with finite-dimensional input. © 2019 V. E. Fedorov, D. M. Gordievskikh, D. Baleanu, and K. Taş.Article Citation - WoS: 36Adaptive Fractional-Order Blood Glucose Regulator Based on High-Order Sliding Mode Observer(inst Engineering Technology-iet, 2019) Heydarinejad, Hamid; Baleanu, Dumitru; Delavari, HadiType I diabetes is described by the destruction of the insulin-producing beta-cells in the pancreas. Hence, exogenous insulin administration is necessary for Type I diabetes patients. In this study, to estimate the states that are not directly available from the Bergman minimal model a high-order sliding mode observer is proposed. Then fractional calculus is combined with sliding mode control (SMC) for blood glucose regulation to create more robustness performance and make more degree of freedom and flexibility for the proposed method. Then an adaptive fractional-order SMC is proposed. The adaptive SMC protect controller against disturbance and uncertainties while the fractional calculus provides robust performance. Numerical simulation verifies that the proposed controllers have better performance in the presence of disturbance and uncertainties without chattering.Article Citation - WoS: 53Citation - Scopus: 58Shehu Transform and Applications To Caputo-Fractional Differential Equations(Etamaths Publ, 2019) Baleanu, Dumitru; Bokhari, Ahmed; Belgacem, RachidIn this manuscript we establish the expressions of the Shehu transform for fractional Riemann-Liouville and Caputo operators. With the help of this new integral transform we solve higher order fractional differential equations in the Caputo sense. Three illustrative examples are discussed to show our approach.