Mostrando recursos 1 - 20 de 324

  1. Existence and Uniqueness of Solution of Stochastic Dynamic Systems with Markov Switching and Concentration Points

    Lukashiv, Taras; Malyk, Igor
    In this article the problem of existence and uniqueness of solutions of stochastic differential equations with jumps and concentration points are solved. The theoretical results are illustrated by one example.

  2. An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game

    Kohli, Ikjyot Singh; Haslam, Michael C.
    We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their stability and derive the Nash equilibria. We also give a detailed account of the local bifurcations that the system exhibits based on choices of the typical Hawk-Dove parameters $v$ and $c$ . We also give details on the connections between the results found in this work and those of the standard two-strategy Hawk-Dove game. We conclude the paper with some examples...

  3. Critical Oscillation Constant for Euler Type Half-Linear Differential Equation Having Multi-Different Periodic Coefficients

    Misir, Adil; Mermerkaya, Banu
    We compute explicitly the oscillation constant for Euler type half-linear second-order differential equation having multi-different periodic coefficients.

  4. Approximate Controllability of Semilinear Control System Using Tikhonov Regularization

    Katta, Ravinder; Sukavanam, N.
    For an approximately controllable semilinear system, the problem of computing control for a given target state is converted into an equivalent problem of solving operator equation which is ill-posed. We exhibit a sequence of regularized controls which steers the semilinear control system from an arbitrary initial state ${x}^{\mathrm{0}}$ to an $\mathrm{ϵ}$ neighbourhood of the target state ${x}_{\tau }$ at time $\tau >\mathrm{0}$ under the assumption that the nonlinear function $f$ is Lipschitz continuous. The convergence of the sequences of regularized controls and the corresponding mild solutions are shown under some assumptions on the system operators. It is also proved that...

  5. An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations

    Cengizci, Süleyman
    In this work, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, we employ a numerical procedure to solve the resulting equations that come from SCEM procedure. In order to show efficiency of this numerical-asymptotic hybrid method, we compare the results with...

  6. Fractional Variational Iteration Method for Solving Fractional Partial Differential Equations with Proportional Delay

    Singh, Brajesh Kumar; Kumar, Pramod
    This paper deals with an alternative approximate analytic solution to time fractional partial differential equations (TFPDEs) with proportional delay, obtained by using fractional variational iteration method, where the fractional derivative is taken in Caputo sense. The proposed series solutions are found to converge to exact solution rapidly. To confirm the efficiency and validity of FRDTM, the computation of three test problems of TFPDEs with proportional delay was presented. The scheme seems to be very reliable, effective, and efficient powerful technique for solving various types of physical models arising in science and engineering.

  7. Existence and Uniqueness of Solutions for BVP of Nonlinear Fractional Differential Equation

    Su, Cheng-Min; Sun, Jian-Ping; Zhao, Ya-Hong
    In this paper, we study the existence and uniqueness of solutions for the following boundary value problem of nonlinear fractional differential equation: $({}^{C}{D}_{\mathrm{0}+}^{q}u)(t)=f(t,u(t))$ ,   $t\in (\mathrm{0,1})$ , $u(\mathrm{0})={u}^{\mathrm{\prime }\mathrm{\prime }}(\mathrm{0})=\mathrm{0},  ({}^{C}{D}_{\mathrm{0}+}^{{\sigma }_{\mathrm{1}}}u)(\mathrm{1})=\lambda ({I}_{\mathrm{0}+}^{{\sigma }_{\mathrm{2}}}u)(\mathrm{1})$ , where $\mathrm{2}\mathrm{0}$ , and $\lambda \ne \mathrm{\Gamma }(\mathrm{2}+{\sigma }_{\mathrm{2}})/\mathrm{\Gamma }(\mathrm{2}-{\sigma }_{\mathrm{1}})$ . The main tools used are nonlinear alternative of Leray-Schauder type and Banach contraction principle.

  8. Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case

    Bernal-Vílchis, Fernando; Hayashi, Nakao; Naumkin, Pavel I.
    We consider the Cauchy problem for the Ostrovsky-Hunter equation ${\partial }_{x}({\partial }_{t}u-(b/\mathrm{3}){\partial }_{x}^{\mathrm{3}}u-{\partial }_{x}\mathcal{K}{u}^{\mathrm{3}})=au$ , $(t,x)\in {\mathbb{R}}^{\mathrm{2}}$ ,   $u(\mathrm{0},x)={u}_{\mathrm{0}}(x)$ , $x\in \mathbb{R}$ , where $ab>\mathrm{0}$ . Define ${\xi }_{\mathrm{0}}={(\mathrm{27}a/b)}^{\mathrm{1}/\mathrm{4}}$ . Suppose that $\mathcal{K}$ is a pseudodifferential operator with a symbol $\stackrel{^}{K}(\xi )$ such that $\stackrel{^}{K}(\pm{\xi }_{\mathrm{0}})=\mathrm{0}$ , $\mathrm{I}\mathrm{m} \stackrel{^}{K}(\xi )=\mathrm{0}$ , and $|\stackrel{^}{K}(\xi )|\le C$ . For example, we can take $\stackrel{^}{K}(\xi )=({\xi }^{\mathrm{2}}-{\xi }_{\mathrm{0}}^{\mathrm{2}})/({\xi }^{\mathrm{2}}+\mathrm{1})$ . We prove the global in time existence and the large time asymptotic behavior of solutions.

  9. A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems

    Ngwane, F. F.; Jator, S. N.
    In this paper, we present a block hybrid trigonometrically fitted Runge-Kutta-Nyström method (BHTRKNM), whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including Hamiltonian systems such as the energy conserving equations and systems arising from the semidiscretization of partial differential equations (PDEs). Four discrete hybrid formulas used to formulate the BHTRKNM are provided by a continuous one-step hybrid trigonometrically fitted method with an off-grid point. We implement BHTRKNM in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which...

  10. A Family of Boundary Value Methods for Systems of Second-Order Boundary Value Problems

    Biala, T. A.; Jator, S. N.
    A family of boundary value methods (BVMs) with continuous coefficients is derived and used to obtain methods which are applied via the block unification approach. The methods obtained from these continuous BVMs are weighted the same and are used to simultaneously generate approximations to the exact solution of systems of second-order boundary value problems (BVPs) on the entire interval of integration. The convergence of the methods is analyzed. Numerical experiments were performed to show efficiency and accuracy advantages.

  11. Modelling the Potential Role of Media Campaigns in Ebola Transmission Dynamics

    Djiomba Njankou, Sylvie Diane; Nyabadza, Farai
    A six-compartment mathematical model is formulated to investigate the role of media campaigns in Ebola transmission dynamics. The model includes tweets or messages sent by individuals in different compartments. The media campaigns reproduction number is computed and used to discuss the stability of the disease states. The presence of a backward bifurcation as well as a forward bifurcation is shown together with the existence and local stability of the endemic equilibrium. Results show that messages sent through media have a more significant beneficial effect on the reduction of Ebola cases if they are more effective and spaced out.

  12. Antisynchronization of Nonidentical Fractional-Order Chaotic Systems Using Active Control

    Bhalekar, Sachin; Daftardar-Gejji, Varsha
    Antisynchronization phenomena are studied in nonidentical fractional-order differential systems. The characteristic feature of antisynchronization is that the sum of relevant state-variables vanishes for sufficiently large value of time variable. Active control method is used first time in the literature to achieve antisynchronization between fractional-order Lorenz and Financial systems, Financial and Chen systems, and Lü and Financial systems. The stability analysis is carried out using classical results. We also provide numerical results to verify the effectiveness of the proposed theory.

  13. Slip Effects on Fractional Viscoelastic Fluids

    Jamil, Muhammad; Khan, Najeeb Alam
    Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions ${}_{p}{\Psi }_{q}$ , by using discrete Laplace transform of the sequential fractional derivatives, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter is $\theta \to 0$ . Furthermore, the solutions for ordinary Maxwell and Newtonian...

  14. Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation

    Berdyshev, A. S.; Karimov, E. T.; Akhtaeva, N.
    Analogs of the Tricomi and the Gellerstedt problems with integral gluing conditions for mixed parabolic-hyperbolic equation with parameter have been considered. The considered mixed-type equation consists of fractional diffusion and telegraph equation. The Tricomi problem is equivalently reduced to the second-kind Volterra integral equation, which is uniquely solvable. The uniqueness of the Gellerstedt problem is proven by energy integrals' method and the existence by reducing it to the ordinary differential equations. The method of Green functions and properties of integral-differential operators have been used.

  15. The Existence of Solutions for a Nonlinear Fractional Multi-Point Boundary Value Problem at Resonance

    Han, Xiaoling; Wang, Ting
    We discuss the existence of solution for a multipoint boundary value problem of fractional differential equation. An existence result is obtained with the use of the coincidence degree theory.

  16. Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition

    Gao, Hongliang; Han, Xiaoling
    By using the fixed point theorem, existence of positive solutions for fractional differential equation with nonlocal boundary condition ${D}_{0+}^{\alpha }u(t)+a(t)f(t,u(t))=0$ , $0

  17. Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions

    Murad, Shayma Adil; Zekri, Hussein Jebrail; Hadid, Samir
    We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.

  18. Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative

    Zhang, Fengrong; Li, Changpin; Chen, YangQuan
    This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.

  19. Malliavin Calculus of Bismut Type for Fractional Powers of Laplacians in Semi-Group Theory

    Léandre, Rémi
    We translate into the language of semi-group theory Bismut's Calculus on boundary processes (Bismut (1983), Lèandre (1989)) which gives regularity result on the heat kernel associated with fractional powers of degenerated Laplacian. We translate into the language of semi-group theory the marriage of Bismut (1983) between the Malliavin Calculus of Bismut type on the underlying diffusion process and the Malliavin Calculus of Bismut type on the subordinator which is a jump process.

  20. An Explicit Numerical Method for the Fractional Cable Equation

    Quintana-Murillo, J.; Yuste, S. B.
    An explicit numerical method to solve a fractional cable equation which involves two temporal Riemann-Liouville derivatives is studied. The numerical difference scheme is obtained by approximating the first-order derivative by a forward difference formula, the Riemann-Liouville derivatives by the Grünwald-Letnikov formula, and the spatial derivative by a three-point centered formula. The accuracy, stability, and convergence of the method are considered. The stability analysis is carried out by means of a kind of von Neumann method adapted to fractional equations. The convergence analysis is accomplished with a similar procedure. The von-Neumann stability analysis predicted very accurately the conditions under which the...

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