Matematik Bölümü Yayın Koleksiyonu

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Now showing 1 - 10 of 25
  • Article
    Citation - WoS: 6
    Citation - Scopus: 8
    Pathological Study on Uncertain Numbers and Proposed Solutions for Discrete Fuzzy Fractional Order Calculus
    (de Gruyter Poland Sp Z O O, 2023) Baleanu, Dumitru; Ma, Chang-You; Shiri, Babak
    A pathological study in the definition of uncertain numbers is carried out, and some solutions are proposed. Fundamental theorems for uncertain discrete fractional and integer order calculus are established. The concept of maximal solution for obtaining a unique uncertain solution is introduced. The solutions of uncertain discrete relaxation equations for the integer and the fractional order are obtained. Various numerical examples are accompanied to clarify the theoretical results and study of uncertain system behavior.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 21
    Generalized Invexity and Duality in Multiobjective Variational Problems Involving Non-Singular Fractional Derivative
    (de Gruyter Poland Sp Z O O, 2022) Kumar, Devendra; Alshehri, Hashim M.; Singh, Jagdev; Baleanu, Dumitru; Dubey, Ved Prakash
    In this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, control of space structures, control of production and inventory, advertising investment, impulsive control problems, mechanics, and several other engineering and scientific problems. The proposed work considers the newly derived Caputo-Fabrizio (CF) fractional derivative operator. It is actually a convolution of the exponential function and the first-order derivative. The significant characteristic of this fractional derivative operator is that it provides a non-singular exponential kernel, which describes the dynamics of a system in a better way. Moreover, the proposed work also presents various weak, strong, and converse duality theorems under the diverse generalized invexity conditions in view of the CF fractional derivative operator.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 12
    Unsteady Nano-Bioconvective Channel Flow With Effect of Nth Order Chemical Reaction
    (de Gruyter Poland Sp Z O O, 2020) Basir, Md Faisal Md; Naganthran, Kohilavani; Azhar, Ehtsham; Mehmood, Zaffar; Mukhopadhyay, Swati; Nazar, Roslinda; Khan, Ilyas; Md Basir, Md Faisal
    Nanofluid bioconvective channel flow is an essential aspect of the recent healthcare industry applications, such as biomedical processing systems. Thus, the present work examined the influence of nth order chemical reaction in an unsteady nanofluid bioconvective channel flow in a horizontal microchannel with expanding/contracting walls. The suitable form of the similarity transformation is exercised to transform the governing boundary layer equations into a more straightforward form of system to ease the computation process. The Runge-Kutta method of fifth-order integration technique solved the reduced boundary layer system and generated the numerical results as the governing parameters vary. It is found that the destructive second-order chemical reaction enhances the mass transfer rate at the lower wall but deteriorates the mass transfer rate at the upper wall. The upper channel wall has a better heat transfer rate than the lower wall when the Reynolds number increases.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Standard Routine Techniques of Modeling of Tick-Borne Encephalitis
    (de Gruyter Poland Sp Z O O, 2020) Arooj, Aroosa; Yasmin, Nusrat; Ghaffar, Abdul; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Ilyas; Akram, Saima
    Tick-borne encephalitis (TBE) is a flaviviral vector-borne disease, which is spread by a tick named Ixodes persulcatus in domestic animals as well as in humans. In this article, susceptible, exposed, infected, recovered model; with no immunity after getting recovered is taken. The only possible immunity is before getting the disease (in our model). The vaccination details are also discussed in the article. Hence, SEIS (susceptible, exposed, infected and again susceptible with zero removal from the specie compartment) is used to construct a mathematical model of TBE. TBE is acute inflammation of the brain parenchyma. After becoming viral in European states and some Asian countries, especially in China, this is an emerging viral disease in Pakistan. After constructing a model, formula for the basic reproduction number R-0-like threshold has been derived by using the next-generation matrix method. The formula for R-0-like threshold is used to evaluate whether the disease is going to be outbroken in the respective area from which the specific data are taken into consideration. The main motivation behind selection of this topic is to address the unawareness of this disease specifically in Pakistan and in its neighboring countries when there persists probability for the outbreak of this disease. Some equilibrium points and their local stability is also discussed. Numerical computations and graphs are also presented to validate the results.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 13
    Quantization of Fractional Harmonic Oscillator Using Creation and Annihilation Operators
    (de Gruyter Poland Sp Z O O, 2021) Rabei, Eqab M.; Al-Jamel, Ahmed; Baleanu, Dumitru; Al-Masaeed, Mohamed
    In this article, the Hamiltonian for the conform-able harmonic oscillator used in the previous study [Chung WS, Zare S, Hassanabadi H, Maghsoodi E. The effect of fractional calculus on the formation of quantum-mechan-ical operators. Math Method Appl Sci. 2020;43(11):6950-67.] is written in terms of fractional operators that we called alpha-creation and alpha-annihilation operators. It is found that these operators have the following influence on the energy states. For a given order alpha, the alpha-creation operator pro-motes the state while the alpha-annihilation operator demotes the state. The system is then quantized using these crea-tion and annihilation operators and the energy eigenvalues and eigenfunctions are obtained. The eigenfunctions are expressed in terms of the conformable Hermite func-tions. The results for the traditional quantum harmonic oscillator are found to be recovered by setting alpha = 1.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 5
    On Some Novel Exact Solutions To the Time Fractional (2+1) Dimensional Konopelchenko-Dubrovsky System Arising in Physical Science
    (de Gruyter Poland Sp Z O O, 2020) Seadawy, Aly R.; Tariq, Kalim U.; Baleanu, Dumitru; Akhtar, Junaid
    The purpose of this article is to construct some novel exact travelling and solitary wave solutions of the time fractional (2 + 1) dimensional Konopelchenko-Dubrovsky equation, and two different forms of integration schemes have been utilized in this context. As a result, a variety of bright and dark solitons, kink- and antikink-type solitons, hyperbolic functions, trigonometric functions, elliptic functions, periodic solitary wave solutions and travelling wave solutions are obtained, and the sufficient conditions for the existence of solution are also discussed. Moreover, some of the obtained solutions are illustrated as two- and three-dimensional graphical images by using computational software Mathematica. These types of solutions have a wide range of applications in applied sciences and mathematical physics. The proposed methods are very useful for solving nonlinear partial differential equations arising in physical science and engineering.
  • Article
    Citation - Scopus: 1
    Magnetic Charged Particles of Optical Spherical Antiferromagnetic Model With Fractional System
    (de Gruyter Poland Sp Z O O, 2021) Korpinar, Talat; Baleanu, Dumitru; Korpinar, Zeliha; Almohsen, Bandar; Inc, Mustafa; Yao, Shao-Wen
    In this article, we first consider approach of optical spherical magnetic antiferromagnetic model for spherical magnetic flows of Upsilon-magnetic particle with spherical de-Sitter frame in the de-Sitter space S-1(2). Hence, we establish new relationship between magnetic total phases and spherical timelike flows in de-Sitter space S-1(2). In other words, the applied geometric characterization for the optical magnetic spherical antiferromagnetic spin is performed. Moreover, this approach is very useful to analyze some geometrical and physical classifications belonging to Upsilon-particle. Besides, solutions of fractional optical systems are recognized for submitted geometrical designs. Geometrical presentations for fractional solu-tions are obtained to interpret the model. These obtained results represent that operation is a compatible and sig-nificant application to restore optical solutions of some fractional systems. Components of models are described by physical assertions with solutions. Additionally, we get solutions of optical fractional flow equations with designs of our results in de-Sitter space S-1(2).
  • Article
    Citation - WoS: 136
    Citation - Scopus: 138
    Lump, Lump-One Stripe, Multiwave and Breather Solutions for the Hunter-Saxton Equation
    (de Gruyter Poland Sp Z O O, 2021) Rizvi, Syed Tahir Raza; Ahmad, Sarfraz; Younis, Muhammad; Baleanu, Dumitru; Seadawy, Aly R.
    The aim of this article was to address the lump, lump-one stripe, multiwave and breather solutions for the Hunter-Saxton equation with the aid of Hirota bilinear technique. This model concerns in a massive nematic liquid crystal director field. By choosing the function f in Hirota bilinear form, as the general quadratic function, trigonometric function and exponential function along with appropriate set of parameters, we find the lump, lump-one stripe, multiwave and breather solutions successfully. We also interpreted some three-dimensional and contour profiles to anticipate the wave dynamics. These newly obtained solutions have some arbitrary constants and so can be applicable to explain diversity in qualitative features of wave phenomena.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 6
    Influence of Interfacial Electrokinetic on Mhd Radiative Nanofluid Flow in a Permeable Microchannel With Brownian Motion and Thermophoresis Effects
    (de Gruyter Poland Sp Z O O, 2020) Nie, Yufeng; Shah, Zahir; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Raees; Khan, Abdul Samad
    In this study, the behavior of a microchannel flow is examined. The fluid is considered to be a nanofluid, which moves between two parallel flat plates in the presence of an electrical double layer. The Buongiorno nanofluid is considered with body force. In this study, the unphysical supposition presented in the preceding work to the discontinuity of the flow fled where the electrostatic potential in the central of the canal must be equal to zero is removed. The incorrect supposition that the pressure constant is preserved, which is considered a known form, is corrected. The current fresh model equation is modified by using dimensionless parameters to convert partial differential equations into ordinary differential equations. The transformed nonlinear equations are solved by the homotopy analysis method. The physical parameters, magnetic parameters, Eckert number, Lewis number, Brownian motion parameters, thermophoresis parameters, and Prandtl number are analyzed. The influence of both the viscous and Joule dissipation in the presence of magneto-hydrodynamic effect is examined.
  • Article
    Citation - WoS: 5
    Exact Solutions of the Laplace Fractional Boundary Value Problems Via Natural Decomposition Method
    (de Gruyter Poland Sp Z O O, 2020) Khan, Hassan; Chu, Yu-Ming; Shah, Rasool; Baleanu, Dumitru; Arif, Muhammad; Hajira
    In this article, exact solutions of some Laplace-type fractional boundary value problems (FBVPs) are investigated via natural decomposition method. The fractional derivatives are described within Caputo operator. The natural decomposition technique is applied for the first time to boundary value problems (BVPs) and found to be an excellent tool to solve the suggested problems. The graphical representation of the exact and derived results is presented to show the reliability of the suggested technique. The present study is mainly concerned with the approximate analytical solutions of some FBVPs. Moreover, the solution graphs have shown that the actual and approximate solutions are very closed to each other. The comparison of the proposed and variational iteration methods is done for integer-order problems. The comparison, support strong relationship between the results of the suggested techniques. The overall analysis and the results obtained have confirmed the effectiveness and the simple procedure of natural decomposition technique for obtaining the solution of BVPs.