Genocchi polynomial method for the multiterm variable-order fractional differential equations

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...

Finite Element Method for Linear Multiterm Fractional Differential Equations

Existence of Positive Solutions for Multiterm Fractional Differential Equations of Finite Delay with Polynomial Coefficients

and Applied Analysis 3 Definition 2.2 see 15 . A cone K is called normal, if there exists a positive constant r such that f, g ∈ K and θ ≺ f ≺ g implies ‖f‖ ≤ r‖g‖, where θ denotes the zero element of K. Definition 2.3 see 16, 17 . Let f : a, b → R, and f ∈ L1 a, b . The left-sided RiemannLiouville fractional integral of f of order α is defined as I af x 1 Γ α ∫x a x − t α−1f t dt, α > 0, x ∈ a...

Discrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients

This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...

Numerical Simulations for Variable-order Fractional Nonlinear Delay Differential Equations

In this paper numerical studies for the variable-order fractional delay differential equations are presented. Adams-Bashforth-Moulton algorithm has been extended to study this problem, where the derivative is defined in the Caputo variable-order fractional sense. Special attention is given to prove the error estimate of the proposed method. Numerical test examples are presented to demonstrate u...