Fractional Integral Inequalities for Generalized Interval-Valued Functions With Applications in Stock Price Prediction via LSTM

We explore the features of fractional integral inequalities for some new classes of interval-valued convex functions (CF s) to establish their generalization compared to the previously known real-valued CF s. Motivated by the foundational role of mathematical inequalities in analysis and optimization, we delve into the formulation and proof of integral inequalities, including Mercer’s inequalities for our newly defined functions. Utilizing Riemann–Liouville fractional integral operators, we further extend our investigation to include variants of Hermite–Hadamard and Hermite–Hadamard–Fejér’s type inequalities, enriching the theoretical landscape of fractional calculus in the context of interval analysis. Under exceptional cases, we produce several well-known results from the related literature. As an application, we introduce a prediction model of stock prices using fractional integral inequalities developed for interval-valued CF s by applying the LSTM model approach and Adam optimizer. Ultimately, we visually represent our findings via specific examples and graphical tools.