This study, considers the fractional order cable model (FCM) in sense of Riemann–Liouville derivatives (R-LFD). We use a modified implicit finite difference approximation to solve FCM numerically. The Fourier series approach is used examine proposed scheme’s theoretical analysis, including stability and convergence. scheme shown be unconditionally stable, approximate solution converges exact so...

In this paper, we use the Riemann-Liouville fractionalintegrals to establish some new integral inequalities related toChebyshev's functional in the case of two differentiable functions.

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by viscosity. This is derived in Riemann variables using a modified finite-gap integration technique for the Ablowitz-Kaup-Newell...

This paper deals with a model for traffic flow based on a system of conservation laws [2]. We construct a solution of the Riemann Problem at an arbitrary junction of a road network. Our construction provides a solution of the full system. In particular, all moments are conserved. AMS subject classifications: 35Lxx, 35L6

The paper deals with a fluid dynamic model for supply chains. A mixed continuum-discrete model is proposed and possible choices of solutions at nodes guaranteeing the conservation of fluxes are discussed. Fixing a rule a Riemann solver is defined and existence of solutions to Cauchy problems is proved.

An extension of the wave propagation algorithm first introduced by LeVeque [J. Comp. Phys. 131, 327–353 (1997)] is developed for hyperbolic systems on a general curved manifold. This extension is important in a variety of applications, including the propagation of sound waves on a curved surface, shallow water flow on the surface of the Earth, shallow water magnetohydrodynamics in the solar tac...

A new multi-state Harten–Lax–van Leer (HLL) approximate Riemann solver for the ideal magnetohydrodynamic (MHD) equations is developed based on the assumption that the normal velocity is constant over the Riemann fan. This assumption is same as that used in the HLLC (‘‘C’’ denotes Contact) approximate Riemann solver for the Euler equations. From the assumption, it is naturally derived that the R...

In this article, we first give a modified Schwarz–Pompeiu formula in general sector ring with angle \(\vartheta =\frac{\pi }{\alpha },\ \alpha \ge 1/2\) by proper conformal mappings, and obtain the solution of Schwarz problem for Cauchy–Riemann equation explicit forms. Furthermore, construct some integral operators discuss their properties detail. Finally, virtue these operators, problems an in...

Abstract In this paper, we study a system of nonlinear Riemann–Liouville fractional differential equations with delays. First, define in an appropriate way initial conditions which are deeply connected the derivative used. We introduce generalization practical stability call time. Several sufficient for time obtained using Lyapunov functions and modified Razumikhin technique. Two types derivati...

We derive two generalizations of Mathisson-Papapetrou-Tulczyjew-Dixon equations from Casalbuoni-Brink-Schwarz type pseudoclassical Lagrangians Majorana spinors on a Riemann-Cartan spacetime. One has "color" freedom, which makes the motion also be generalization Wong equations. The other is spinor model coupled with Rarita-Schwinger field to preserve supersymmetry. coupling torsion modified due ...