This study introduces a novel numerical approach that utilizes orthonormal Bell polynomials (OBPs) and block-pulse functions (BPFs) to address the fractional model of HIV infection in \(\text {CD4}^{+}\) T cells. The model consists of three fractional nonlinear ordinary differential equations. The initial phase of this approach involves orthonormalizing the Bell polynomials using the Gram-Schmidt algorithm. Following this, BPFs are used to create an operational matrix related to fractional integration for OBPs. By utilizing this matrix, the problem is transformed into a series of nonlinear algebraic equations. These equations can be effectively solved using an appropriate numerical technique, such as Newton’s method. Ultimately, the numerical results illustrate the method’s applicability, efficiency, and accuracy, and these findings are compared with existing methods documented in the literature.
