Affiliation:
1. Department of Mathematics, Faculty of Applied Science King Mongkuts University of Technology North Bangkok 1518 Pracharat 1 Road,Wongsawang, Bangsue Krungthep Mahanakorn 10800, THAILAND
Abstract
Nowadays, integration is one of the trending fields applied in calculus, especially in partial differential equations. Researchers are contributing to support useful utilities to solve partial differential equations in many kinds of methods. In this paper, we perform an application of Volterra Integral Equations in a reduced differential transform method (we call VIE-RDTM) to find the approximate solutions of partial differential equations. The aim is to find the approximate solutions approach to the exact solutions with more general forms. We also extend some new results for basic functions and compare the solutions using the reduced differential transform method and VIE-RDTM by depicting the approximate solutions in some partial differential equations. The results showed that the VIE-RDTM method gets the state-of-the-art general form of the solutions when the errors approach zero.
Publisher
World Scientific and Engineering Academy and Society (WSEAS)
Reference52 articles.
1. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations theory and applications of fractional differential equations, (Elsevier B.V., 2006) 1st ed.
2. A. B. Malinowska, T. Odzijewicz, and D. F. Torres, Advanced methods in the fractional calculus of variations, SpringerBriefs in Applied Sciences and Technology, 2015.
3. S. G. Georgiev, Fractional dynamic calculus and fractional dynamic equations on time scales, Springer International Publishing AG part of Springer Nature, 2018.
4. V. E. Tarasov, Fractional dynamics applications of fractional calculus to dynamics of particles, fields and media, (Springer is part of Springer SClence+Busmess Media, 2010) Chap. 1-2.
5. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional integrals and derivatives: Theory and applications, (Gordon and Breach Science Publishers S .A., 1993) Chap. 1-4.