<p>The present study aims to formulate a new class of nonlinear programming problems. Here, pseudo-convexity and quasi-convexity are defined using Caputo fractional derivative, which is the generalization form of classical definitions. Also, Taylor series expansion of the function of several variables are derived using the same Caputo fractional derivative. Thereafter, the above concepts are used to develop a Mond-Weir type dual model, where the objective function is fractional order pseudo-convex and constraints functions are fractional order quasi-convex. Appropriate duality (weak, strong, and converse) theorems are established and proved between the primal and corresponding Mond-Weir type dual. In addition, several graphs and numerical examples are constructed to justify the efficacy of the new findings.</p>