Abstract
The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the k-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how q-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role.
Highlights
The idea of convex analysis has a strong background and has been the inspiration for excellent research for more than a century in the field of mathematics
Variations, and speculations of the theory of convexity have been taken into consideration by numerous researchers. This theory develops and provides numerical procedures to handle and study complex problems in the field of mathematics. This theory has been very inspirational and popular among mathematicians as it possesses a wide range of potential applications in pure and applied sciences
The correlation between convexity and inequalities has acquired a great deal of consideration among mathematicians because of their basic definitions and properties
Summary
The idea of convex analysis has a strong background and has been the inspiration for excellent research for more than a century in the field of mathematics. Variations, and speculations of the theory of convexity have been taken into consideration by numerous researchers This theory develops and provides numerical procedures to handle and study complex problems in the field of mathematics. The theory of inequalities is still intensively developed In this regard, the Hermite-Hadamard type inequality is broadly notable and has been read and generalized for various sorts of convex functions under different parameters and conditions. Fractional differentiable inequalities have applications in fractional differential equations, the most important ones being to establish the uniqueness of the solution of initial-value problems and give upper bounds to their solution These applications have motivated many researchers in the field of integral inequalities to investigate a few extensions and generalizations using different fractional differential and integral operators. Some interesting applications related to q-digamma functions are discussed
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