solvability of an infinite system of the fractional order non-linear fractional hadamard functional integral equations in the banach algebra (c(j))∞

In the present paper, we investigate the existence of solutions of an infinite system of the fractional order non-linear hadamard functional integral equations. the problem is discussed in the sequence banach algebra (c(j))∞ (j is a bounded interval), using the theory of measure of non-compactness together with the fixed point theory in banach algebras. an example is provided to support our main result.