Abstract
AbstractIn this article, we have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation. The fractional derivatives are described in the Caputo sense. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, the systems of nonlinear algebraic equation is derived. We further solve the system of nonlinear algebraic equation using Maple 13 and thus obtain the coefficients of the generalized Taylor expansion. Illustrative examples are presented to demonstrate the effectiveness of the proposed method.
Highlights
The concept of fractional or noninteger order derivation and integration can be traced back to the genesis of integer order calculus itself [1, 2]
We present numerical and analytical solutions for the fractional Riccati differential equation with delay term
Where A(x), B(x), and C(x) are given functions, α is a parameter describing the order of the fractional derivative and λ, β are appropriate constants, and λx + β > 0 for all x ∈ [0, 1]
Summary
The concept of fractional or noninteger order derivation and integration can be traced back to the genesis of integer order calculus itself [1, 2]. We present numerical and analytical solutions for the fractional Riccati differential equation with delay term. In modern applications (see e.g., [11]) much more general values of the order appear in the equations, and one needs to consider numerical and analytical methods to solve differential equations of arbitrary order. This equation is solved the numerically in [12,13,14]. This equation is solved, we obtained the coefficients, the approximate solutions for various N.
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