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By using the Adomian method [55, 56] we propose, for the solution of the Volterra integral equation (1.3), the series of expansion functions given by y(t) = sum_{n=0}^{+infty} y_{n}(t) and we obtain the following recurrence expansions: y_{0}(t) = 1, quad y_{n}(t) = -{2lambdaover sqrt{pi}} int _{0}^{t} y_{n-1} tau) sqrt{t-tau},dtau, quadforall ngeq1.
Following the idea of [25 33], we propose, for the solution of integral equation (3.24), the series of expansion functions given by begin{aligned} y(t) = sum_{n=0}^{+infty} y_{n}(t), end{aligned} (3.28) and we obtain the following recurrence expressions: begin{aligned} y_{0}(t)=1, qquad y_{n}(t)= - {2lambdaover sqrt{pi}} int_{0}^{t} y_{n-1} tau) sqrt{t-tau},d tau, quadforall n geq1.
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