Some scientific pieces of research are governed by classes of partial integro-differential equations (PIDEs) of fractional order that are leading to novel challenges in simulation and optimization. In this chapter, a soft numerical algorithm is proposed and analyzed to fitted analytical solutions of PIDEs with appropriate initial and Neumann conditions in Sobolev space. Meanwhile, the solutions are represented in series form with strictly computable components. By truncating n-term approximation of the analytical solution, the solution methodology is discussed for both linear and nonlinear problems based on the nonhomogeneous term. Analysis of convergence and smoothness are given under certain assumptions to show the theoretical structures of the method. Dynamic features of the approximate solutions are studied through an illustrated example. The yield of numerical results indicates the accuracy, clarity, and effectiveness of the proposed algorithm as well as provide a proper methodology in handling such fractional issues.
|Journal||Data powered by TypesetAdvanced Theory and Applications of Fractional Calculus (pp.107-119)|
|Publisher||Data powered by TypesetSpringer Singapore|