Advanced Mathematical Models & Applications

Convexity plays a central role in establishing bounds for integral inequalities, allowing precise estimation of functions over a domain. Recent developments in fractional calculus and generalized convexity have revealed strong links between new integral operators and inequalities. In this paper, we explore a lemma with help of Katugampola fractional operator. In addition, we developed some Ostrowski-type inequalities on the basis of lemma by employing (m, n)-polynomial (p₁, p₂) -convex functions defined on the coordinates pertaining to Katugampola fractional operator. We present some remarks via Hadamard and Riemann-Liouville fractional operator. Furthermore, we present some practical applications in image processing and signal analysis (bivariate interpolation error bounds and fractional order image filtering), heat transfer and diffusion processes (temperature distribution bounds and energy functional estimates), and economics (two-commodity utility functions, marginal rate of substitution estimates and optimal consumption under budget constraints). These additions provide clear applied insight and demonstrate that the proposed generalization is both meaningful and relevant beyond purely algebraic considerations. The results obtained not only broaden existing inequalities but also capture recent findings as special cases, demonstrating both generality and practical relevance in multi-dimensional analysis.