The fractional Langevin equation has more advantages than its classical in representing the random motion of Brownian particles complex viscoelastic fluid. Mittag–Leffler (ML) without singularity is accurate and effective Riemann–Caputo (RC) Riemann–Liouville (RL) portraying motion. This paper focuses on a nonlinear ML-fractional system with distributed lag integral control. Employing fixed-poi...

is called Fuchsian if the N ×N coefficient matrix A(λ) is a rational function of λ whose singularities are simple poles. Each Fuchsian system generates, via analytic continuation of its fundamental solution Ψ (λ) along closed curves, a representation of the fundamental group of the punctured Riemann sphere (punctured at the poles of A(λ)) in the group of N ×N invertible matrices. This represent...

A two-dimensional Riemann solver is proposed for the solution of hyperbolic systems of conservation laws in two dimensions of space. The solver approximates the solution of a so-called angular two-dimensional Riemann problem as the weighted sum of the solutions of one-dimensional Riemann problems. The weights are proportional to the aperture of the regions of constant state. The two-dimensional...

In this paper, we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military b...

The Riemann-Lanczos problem for 4-dimensional manifolds was discussed by Bampi and Caviglia. Using exterior differential systems they showed that it was not an involutory differential system until a suitable prolongation was made. Here, we introduce the alternative Janet-Riquier theory and use it to consider the Riemann-Lanczos problem in 2 and 3 dimensions. We find that in 2 dimensions, the Ri...

We are solving the classical Riemann-Hilbert problem of rank N > 1 on the extended complex plane punctured in 2m + 2 points, for N × N quasi-permutation monodromy matrices with 2m(N − 1) parameters. Our approach is based on the finite gap integration method applied to study the Riemann-Hilbert by Deift, Its, Kapaev and Zhou [1] and Kitaev and Korotkin [2, 3]. This permits us to solve the Rieman...

We present an extension of the HLLC approximate Riemann solver by Toro, Spruce and Speares to the relativistic equations of fluid dynamics. The solver retains the simplicity of the original two-wave formulation proposed by Harten, Lax and van Leer (HLL) but it restores the missing contact wave in the solution of the Riemann problem. The resulting numerical scheme is computationally efficient, r...