Solvability and iterative approximation of an infinite system of two-variable Hadamard-type fractional integral equations in ℓp space

In this paper, we examine an infinite system of two-variable functional integral equations involving Hadamard fractional integral operator. The analysis is carried out in the Banach sequence space ${\ell }_p,\text{for}p>1$. The primary objective of this study is to establish the existence of solutions based on certain assumptions using the Meir–Keeler condensing operator and the theory of measures of non-compactness. To support the theoretical results, we provide a concrete example. Furthermore, we construct an iterative algorithm by utilizing two semi-analytical methods-the modified homotopy perturbation method (abbreviated as MHPM) and Adomian’s decomposition method (abbreviated as ADM) to compute approximate solutions. A rigorous convergence analysis confirms that the sequence generated by the proposed algorithm converges in the ${\ell }_p$-norm. In addition, we perform a stability analysis to examine the sensitivity of the solution under initial data perturbations. Numerical results validate the theoretical findings and demonstrate the high accuracy and efficiency of the proposed method.