Subordination Principle for a Class of Fractional Order Differential Equations

Subordination Principle for a Class of Fractional Order Differential Equations

The fractional order differential equation u′(t) = Au(t) + γD t Au(t) + f(t), t > 0, u(0) = a ∈ X is studied, whereA is an operator generating a strongly continuous one-parameter semigroup on a Banach space X , D t is the Riemann–Liouville fractional derivative of order α ∈ (0, 1), γ > 0 and f is an X-valued function. Equations of this type appear in the modeling of unidirectional viscoelastic ...

Computational Method for Fractional-Order Stochastic Delay Differential Equations

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

A numerical method for solving a class of distributed order time-fractional diffusion partial differential equations according to Caputo-Prabhakar fractional derivative

In this paper, a time-fractional diffusion equation of distributed order including the Caputo-Prabhakar fractional derivative is studied. We use a numerical method based on the linear B-spline interpolation and finite difference method to study the solutions of these types of fractional equations. Finally, some numerical examples are presented for the performance and accuracy of the proposed nu...

The variational iteration method for a class of tenth-order boundary value differential equations

Theory of Hybrid Fractional Differential Equations with Complex Order

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...