Here ordinary differential equations of third and higher order are considered; in particular, a class of equations which can be solved by quadratures is exploited. Indeed, crucial to obtain our result is the property of the Riccati equation, according to which, given one particular solution, then its general solution can be determined explicitly. Thus, what we term the “Riccati” Property is int...

The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of nonlinear, ordinary differential equation with derivative fractional variable order Gerasimov–Caputo type. questions approximation, convergence, and stability this are studied. It is shown that conditionally stable converges to first order. Using Riccati as an example, computational accuracy method a...

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

We study a class of rational matrix differential equations that generalize the Riccati differential equations. The generalization involves replacing positive definite “weighting” matrices in the usual Riccati equations with either semidefinite or indefinite matrices that arise in linear quadratic control problems and differential games−both stochastic and deterministic. The purpose of this pape...

By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.

this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...