In this paper a higher-order numerical solution of a non-linear Volterra integro-differential equation is discussed. Example of this question has been solved numerically using the Runge-Kutta-Verner method for Ordinary Differential Equation (ODE) part and Newton-Cotes formulas for integral parts.

The existence-uniqueness criteria of nonlinear fractional integro-differential equations variable order with multiterm boundary value conditions are considered in this work. By utilizing the concepts generalized intervals combined piecewise constant functions, we transform our problem into usual Caputo’s differential order. We develop necessary for assuring solution's existence and uniqueness b...

In this manuscripts, we consider the coupled differential-integral equations including variable-order Caputo fractional operator. To solve numerically these type of equations, apply shifted Jacobi-Gauss collocation scheme. Using numerical method a system algebraic is constructed. We with recursive in nonlinear case and it linear formulas. Finally, for high performance suggested three Examples a...