Solvability of Langevin equations with two Hadamard fractional derivatives via Mittag–Leffler functions

Local stable manifold of Langevin differential equations with two fractional derivatives

*Correspondence: [email protected]; [email protected]; [email protected] 1Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P.R. China 2School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland Abstract In this paper, we investigate the existence of local center stable manifolds of Langevin differential equations wi...

Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions

We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical pr...

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

Numerical Calculation of Fractional Derivatives for the Sinc Functions via Legendre Polynomials

‎This paper provides the fractional derivatives of‎ ‎the Caputo type for the sinc functions‎. ‎It allows to use efficient‎ ‎numerical method for solving fractional differential equations‎. ‎At‎ ‎first‎, ‎some properties of the sinc functions and Legendre‎ ‎polynomials required for our subsequent development are given‎. ‎Then‎ ‎we use the Legendre polynomials to approximate the fractional‎ ‎deri...

Solvability of Context Equations with two

Context uniication is a natural variant of second order uniica-tion that represents a generalization of word uniication at the same time. While second order uniication is wellknown to be undecidable and word uniication is decidable it is currently open if solvability of context equations is decidable. We show that solvability of systems of context equations with two context variables is decidab...