A fractional B-spline collocation method for the numerical solution of fractional predator-prey models

We present a collocation method based on fractional B-splines for the solution of fractional differential problems. The key-idea is to use the space generated by the fractional B-splines, i.e., piecewise polynomials of noninteger degree, as approximating space. Then, in the collocation step the fractional derivative of the approximating function is approximated accurately and efficiently by an exact differentiation rule that involves the generalized finite difference operator. To show the effectiveness of the method for the solution of nonlinear dynamical systems of fractional order, we solved the fractional Lotka-Volterra model and a fractional predator-pray model with variable coefficients. The numerical tests show that the method we proposed is accurate while keeping a low computational cost

A Generalized Version of a Low Velocity Impact between a Rigid Sphere and a Transversely Isotropic Strain-Hardening Plate Supported by a Rigid Substrate Using the Concept of Noninteger Derivatives

A low velocity impact between a rigid sphere and transversely isotropic strain-hardening plate supported by a rigid substrate is generalized to the concept of noninteger derivatives order. A brief history of fractional derivatives order is presented. The fractional derivatives order adopted is in Caputo sense. The new equation is solved via the analytical technique, the Homotopy decomposition method (HDM). The technique is described and the numerical simulations are presented. Since it is very important to accurately predict the contact force and its time history, the three stages of the indentation process, including (1) the elastic indentation, (2) the plastic indentation, and (3) the elastic unloading stages, are investigated

Analytic structure of scalar composites in the symmetric phase of the gauged Nambu-Jona-Lasinio model

The gauged Nambu-Jona-Lasinio model in the quenched-ladder approximation has non-trivial dynamics near a critical scaling region (critical curve) separating a chiral symmetric and a dynamically chiral symmetry broken phase. Scalar and pseudoscalar composites corresponding to the four-fermion interaction become relevant degrees of freedom at short distances, which is reflected in the appearance of a large anomalous dimension of the four-fermion operators. A method is introduced for solving the Schwinger-Dyson equation for the Yukawa vertex in specific kinematic regimes. This allows one to derive an analytic expression for the scalar propagator, which is valid along the entire critical curve. The mass and width of the scalar composites in the critical scaling region are reexamined and the conformal phase transition at the critical gauge coupling is discussed.Comment: final version to appear in Phys. Rev.

New Integrable Sectors in Skyrme and 4-dimensional CP^n Model

The application of a weak integrability concept to the Skyrme and $CP^n$ models in 4 dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic solutions, is derived. This procedure can be applied to the massive Skyrme model, as well. Moreover, an example of a family of chiral Lagrangians providing exact, finite energy Skyrme-like solitons with arbitrary value of the topological charge, is given. In the case of $CP^n$ models a tower of integrable subsystems is obtained. In particular, in (2+1) dimensions a one-to-one correspondence between the standard integrable submodel and the BPS sector is proved. Additionally, it is shown that weak integrable submodels allow also for non-BPS solutions. Geometric as well as algebraic interpretations of the integrability conditions are also given.Comment: 23 page