Shifted Legendre polynomials (SLPs) with the Riemann–Liouville fractional integral
operator have been used to create a novel fractional integration tool. This tool will be called …

We introduce a hybrid Gegenbauer (ultraspherical) integration method (HGIM) for solving
boundary value problems (BVPs), integral and integro-differential equations. The proposed …

In this article, we use the operation matrix (OM) of Riemann–Liouville fractional integral of
the shifted Gegenbauer polynomials with the Lagrange multiplier method to provide efficient …

This paper introduces a new approach for solving fractional differential algebraic equations
(FDAEs) by using the operational matrix of Riemman Liouville (RL) fractional integral of the …

This paper introduces a new numerical mechanism for solving multi-order fractional
differential equations (MOFDEs) and systems of fractional differential equations, in which the …

Analytic solutions of simple optimal control problems may be found using classical tools
such as the calculus of variations, dynamic programming or the minimum principle …

This study presents a new numerical approach for solving fractional-order pantograph
partial-differential equations, in which the fractional derivatives are expressed in the Caputo …

The theory of Gegenbauer (ultraspherical) polynomial approximation has received
considerable attention in recent decades. In particular, the Gegenbauer polynomials have …

In this paper, numerical solution depending on Lagrange cardinal operational collocation
optimization method (LCOCOM) is introduced. The LCOCOM is developed to obtain the …

The main core of this paper is to analyze the application of the quarter-sweep iterative
concept on finite difference and composite trapezoidal schemes with Gauss-Seidel iterative …