Recursos de colección
Misir, Adil; Mermerkaya, Banu
We compute explicitly the oscillation constant for Euler type half-linear second-order differential equation having multi-different periodic coefficients.
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...
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...
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.
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.
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.
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...
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.
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.
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.
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...
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.
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.
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
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.
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.
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.
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...
Rida, S. Z.; Arafa, A. A. M.
We develop a new application of the Mittag-Leffler Function method that will extend the application of the method to linear differential equations with fractional order. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving linear differential equations of fractional order.
Effati, Sohrab; Saberi Nik, Hassan; Buzhabadi, Reza
The homotopy analysis method (HAM) is employed to obtain symbolic approximate solutions for nonlinear coupled equations with parameters derivative. These nonlinear coupled equations with parameters derivative contain many important mathematical physics equations and reaction diffusion equations. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The efficiency and accuracy of the method are verified by using two famous examples: coupled Burgers and mKdV equations. The obtained results show that the homotopy perturbation method is a special case of homotopy analysis method.