University of MaraghehSahand Communications in Mathematical Analysis2322-5807Articles in Press20230822Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex Function70715910.22130/scma.2022.537502.976ENAliHassanDepartment of Mathematics, Shah Abdul Latif University Khairpur-66020, Pakistan.0000-0003-1648-337XAsif R.KhanDepartment of Mathematics, University of Karachi, University Road, Karachi-75270, Pakistan.0000-0002-4700-4987Journal Article20210825In this paper, we aim to state well-known Ostrowski inequality via fractional Montgomery identity for the class of $\phi-\lambda-$ convex functions. This generalized class of convex function contains other well-known convex functions from literature, allowing us to derive Ostrowski-type inequalities as specific instances. Moreover, we present Ostrowski-type inequalities for which certain powers of absolute derivatives are $\phi-\lambda-$ convex using various techniques, including Hölder's inequality and the power mean inequality. Consequently, various established results would be captured as special cases. Moreover, we provide applications in terms of special means, allowing us to derive many numerical inequalities related to special means from Ostrowski-type inequalities.