Abstract
In this paper, we proved the existence and uniqueness and convergence of the solution of new type for nonlinear fuzzy volterra integral equation . The homotopy analysis method are proposed to solve the new type fuzzy nonlinear Volterra integral equation . We convert a fuzzy volterra integral equation for new type of kernel for integral equation, to a system of crisp function nonlinear volterra integral equation . We use the homotopy analysis method to find the approximate solution of the system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy volterra integral equation . Some numerical examples is given and results reveal that homotopy analysis method is very effective and compared with the exact solution and calculate the absolute error between the exact and AHM .Finally using the MAPLE program to solve our problem .
Highlights
The solutions of integral equations have a major role in the field of science and engineering
Borzabadi and Fard in [5] obtained a numerical solution of nonlinear Fredholm integral equations of the second kind.The concept of fuzzy numbers and fuzzy arithmetic operations were first introduced by Zadeh [14],Dubois and Prade [21]
Babolian et al and Abbasbandy et al in [10,11] obtained a numerical solution of linearFredholm fuzzy integral equations of the second kind, while finding an approximate solution for the fuzzynonlinear kinds.is more difficult and a numerical method in this case can be found in [4]In this paper, we present a novel and very numerical method ( Homotopy Analysis method ) for solving fuzzy nonlinear volterra integral equation
Summary
The solutions of integral equations have a major role in the field of science and engineering. Borzabadi and Fard in [5] obtained a numerical solution of nonlinear Fredholm integral equations of the second kind.The concept of fuzzy numbers and fuzzy arithmetic operations were first introduced by Zadeh [14],Dubois and Prade [21]. A fuzzy number u in parametric form is a pair (u, u)of function u(α), u(α) , satisfies the following requiremenst: i) u(α) is a bounded left continuous non- decreasing function over [0, 1]. If the fuzzy function f t is continuous in metric D,its definite the integral exists and We explain homotopy analysis methods as approximating solution of this system of nonlinear integral equations in crisp case. We explain homotopy analysis methods as approximating solution of this system of nonlinear integral equations in crisp case. we find approximate solutions for u(x), a ≤ x ≤ b 0 ≤ c ≤ x
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