Islamic banks are financial intermediaries with the claim of being an alternative to commercial banks. Recently a considerable literature has been produced around the theme of whether or not the alternative presented in theory has been reflected in practice. However, these studies are exploratory and interpretative in nature. The quantitative researches presented thus by far provide indirect evidence for the central theoretical issue. To date, very little attention has been paid to the role of the relationship between interest rates and profit-share accruals. These studies have also suffered from shortcomings with regards to the methods applied. The primary aim of this paper is to provide empirical and theoretical evidence to the claim of Islamic banks to be alternative to commercial banks. It does so by investigating the relationship between profit share accruals and deposit rates by employing wavelet coherence method for the first time. This study uses longitudinal monthly data for the 2000 to 2018 period, particularly from Turkey, and provides an exciting opportunity to advance our knowledge about the structure of Islamic banking with focusing specifically on fund supply. The results have revealed that Islamic banks are an alternative to fund suppliers in short-term. In addition long-term maturities had shown a strong alternative characteristic in the pre-2006 period; however, they were unable to preserve it in the post-2006 period after the effectiveness of Banking Act No. 5411. Findings also show bidirectional causalities to be found in different periods. The findings have important implications for the market players and policy makers.