A Symbolic Method for Solving a Class of Convolution-Type Volterra–Fredholm–Hammerstein Integro-Differential Equations under Nonlocal Boundary Conditions

Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science engineering. Nonlocal boundary conditions more effective, some cases necessary, because they accurate measurements of the true state than classical (local) initial conditions. Closed-form solutions always desirable, not only efficient, but also can be valuable benchmarks for validating approximate numerical procedures. This paper presents a direct operator method solving, closed form, class Volterra–Fredholm–Hammerstein-type integro-differential under nonlocal when inverse associated exists found explicitly. A technique constructing convolution-type (VIDEs) multipoint integral is provided. The proposed methods suitable integration into any computer algebra system. Several linear nonlinear examples solved demonstrate effectiveness method.