Spectral-Collocation Methods for Fractional Pantograph Delay-Integrodifferential Equations

Polynomial spline collocation methods for second-order Volterra integrodifferential equations

where q : I → R, pi : I → R, and ki : D → R (i = 0,1) (with D := {(t,s) : 0 ≤ s ≤ t ≤ T}) are given functions and are assumed to be (at least) continuous in the respective domains. For more details of these equations, many other interesting methods for the approximated solution and stability procedures are available in earlier literatures [1, 3, 4, 5, 6, 7, 8, 11]. The above equation is usually...

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

Spectral-collocation Method for Fractional Fredholm Integro-differential Equations

We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of FredholmVolterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L∞ norm and weighted L2-norm. The numerical examp...

A New Generalized Laguerre-gauss Collocation Scheme for Numerical Solution of Generalized Fractional Pantograph Equations

A.H. BHRAWY1,2, A.A. AL-ZAHRANI3, Y.A. ALHAMED3, D. BALEANU3,4,5 1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia E-mail: [email protected] 2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt 3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, J...