[PDF] Top 20 A unique continuous solution for the Bagley-Torvik equation

... the Bagley-Torvik equation with coordinate derivatives of non-integer order ...HPM solution, as applied to this type of equations have been thor- oughly ... See full document

... The organization of the rest of this paper is as follows: In Section 2, we introduce some necessary definitions and mathematical preliminaries of sinc functions, fractional calculus and Gauss-Jacobi quadrature. In Section ... See full document

... In this paper, Chelyshkov operational matrix of fractional derivative has been derived. Our approach was based on the tau method. The proposed technique is easy to implement efficiently and yield accurate results. ... See full document

... analytical solution involves the evaluation of a convolution integral, containing a Green’s function expressed as an infinite sum of derivatives of Mittag–Leffler functions, and for general functions f this cannot ... See full document

... Abstract : Local polynomial smoother (LPS) is a weighted local least-squares nonpara- metric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential ... See full document

... the Bagley- Torvik ...the solution of this problem and proposed a numerical method in his ...the Bagley-Torvik equation and obtained the same solution as Podlubny’s ... See full document

... where g(t) is chosen such that the exact solution of Eq. (.) is f (t) = sin(αt). We apply FTM for various values of α and M. Table  displays the comparison between the results obtained by FTM with those ... See full document

... locally unique solution x ∗ of the equation F(x) + G(x) = 0, where F and G are continuous operators defined on an open convex subset D of a Banach space X with values in a Banach space Y ... See full document

... differential equation with Markovian switching to have a unique global ...time) solution for any given initial data, the coefficients of the equation are generally required to satisfy the ... See full document

... numerical solution to the generalized B–T equa- ...B–T equation with the fractional order 1 < α < 2 was ...B–T equation with fractional integral boundary conditions and the frac- tional order 0 ... See full document

... analytical solution of the Bagley-Torvik equation with homogeneous initial conditions by using Green’s ...analytical solution of the Bagley-Torvik ...the ... See full document

... Step 3: Further we Assume suitable collocation point for Equation (7). There- fore, we obtained system has M + 1 equations and M + 1 unknowns. Solving this system gives the unknown coefficients using Conjugate ... See full document

... PD equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary ... See full document

... the equation x + Ax = f where A is a Lipschitz accretive operator defined on p-uniformly smooth Banach space ...the unique solution of the equation x + Ax = f under slightly dif- ferent ... See full document

... a unique strong solution for the Cauchy problem to semilinear nondegenera- te fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential ... See full document

... elliptic equation (1.5) although the equation can be transferred to a Laplace equation ...elliptic equation, but the transferred version may or may not be defined for the resulting Laplace ... See full document

... lower cost for any fixed z. In addition, a higher κ also induces more agents to invest, as the equilibrium cut-off agent given by 8.3 is decreasing in κ, so that the high regime is also more likely for endogenous ... See full document

... In this study we prove the continuous dependence of the solution u = u(x, t) upon the data ϕ(x) and f (x, t, u). In [], a similar iteration method is used with this kind of a local boundary condition for a ... See full document

... trivial solution in a semilinear parabolic equation with con- tinuous, increasing nonlinearity f ...evolution equation; (c) monotonicity of the semigroup S β ... See full document

... a solution of an equation with respect to perturbations is called the variation formula of solution (variation ...approximate solution of the perturbed equa- tion in an analytical form on the ... See full document