An Application of Multiple Erdélyi–Kober Fractional Integral Operators to Establish New Inequalities Involving a General Class of Functions

Abstract

This research aims to develop generalized fractional integral inequalities by utilizing multiple Erdélyi–Kober (E–K) fractional integral operators. Using a set of j, with (j∈N) positively continuous and decaying functions in the finite interval a≤t≤x, the Fox-H function is involved in establishing new and novel fractional integral inequalities. Since the Fox-H function is the most general special function, the obtained inequalities are therefore sufficiently widespread and significant in comparison to the current literature to yield novel and unique results.

Keywords

• Fox-H function
• generalized inequalities
• multiple Erdélyi–Kober (E–K) fractional integral transforms
• continuous functions
• mathematical operators