Explicit iteration of an unbounded solution of turbulent flow model involving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si359.svg" display="inline" id="d1e75"><mml:mi>ψ</mml:mi></mml:math>-Riemann–Liouville fractional derivativ

This paper is concerned for the first time an explicit iteration of an unbounded solution for a turbulent flow model involving ψ-Riemann–Liouville fractional derivatives with the p-Laplacian operator on the infinite interval [a,∞),a≥0. A suitable Banach space for our analysis is defined. The fractional integral formula that corresponds to the suggested problem is also derived. The existence and uniqueness results of an unbounded solution for a such model are proved by utilizing the classical Banach contraction technique. Several types of the Ulam–Hyers stability are discussed. The properties of the p-Laplacian operator with unbounded domains created enormous challenges and difficulties. At the end, illustrative examples are enhanced to examine the main findings.