Eigenfunctions and fundamental solutions of the fractional two-parameter Laplacian.
Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains
Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.
Ergodicity of hypoelliptic SDEs driven by fractional brownian motion
We demonstrate that stochastic differential equations (SDEs) driven by fractional brownian motion with Hurst parameter H>½ have similar ergodic properties as SDEs driven by standard brownian motion. The focus in this article is on hypoelliptic systems satisfying Hörmander’s condition. We show that such systems enjoy a suitable version of the strong Feller property and we conclude that under a standard controllability condition they admit a unique stationary solution that is physical in the...
Erratum to “Mittag-Leffler stability theorem for fractional nonlinear systems with delay”.
Eulerian numbers with fractional order parameters.
Existence and attractivity for fractional order integral equations in Fréchet spaces
In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Riemann-Liouville fractional order, by using an extension of the Burton-Kirk fixed point theorem in the case of a Fréchet space.
Existence and uniqueness of fractional differential equations with integral boundary conditions.
Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
We study the existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. Examples are provided to illustrate the main results.
Existence and uniqueness of mild solution for fractional integrodifferential equations.
Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order
Two-term semi-linear and two-term nonlinear fractional differential equations (FDEs) with sequential Caputo derivatives are considered. A unique continuous solution is derived using the equivalent norms/metrics method and the Banach theorem on a fixed point. Both, the unique general solution connected to the stationary function of the highest order derivative and the unique particular solution generated by the initial value problem, are explicitly constructed and proven to exist in an arbitrary...
Existence and uniqueness of solutions for the fractional integro-differential equations in Banach spaces.
Existence and uniqueness of solutions to fractional semilinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions.
Existence of convex and non convex local solutions for fractional differential inclusions.
Existence of local and global solutions to some impulsive fractional differential equation.
Existence of positive solution of a singular partial differential equation
Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.
Existence of positive solutions for fractional differential equations with Riemann-Liouville left-hand and right-hand fractional derivatives.
Existence of positive solutions for multiterm fractional differential equations of finite delay with polynomial coefficients.
Existence of positive solutions for multi-term non-autonomous fractional differential equations with polynomial coefficients.
Existence of positive solutions for singular fractional differential equations.
Existence of solutions for fractional differential inclusions with antiperiodic boundary conditions.