Open AccessUsage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind
Author(s) -
Ahmed A. Hamoud,
Kirtiwant P. Ghadle
Publication year - 2018
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.49.2018.2718
Subject(s) - mathematics , homotopy analysis method , uniqueness , convergence (economics) , fredholm integral equation , work (physics) , integral equation , volterra equations , volterra integral equation , reliability (semiconductor) , mathematical analysis , homotopy , nonlinear system , pure mathematics , mechanical engineering , power (physics) , physics , engineering , quantum mechanics , economics , economic growth
The reliability of the homotopy analysis method (HAM) and reduction in the size of the computational work give this method a wider applicability. In this paper, HAM has been successfully applied to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. Also, the behavior of the solution can be formally determined by analytical approximation. Moreover, the study proves the existence and uniqueness results and the convergence of the solution. This paper concludes with an example to demonstrate the validity and applicability of the proposed technique.