NEW DEVELOPMENTS OF FRACTIONAL INTEGRAL INEQUALITIES VIA DIFFERENT TYPES OF CONVEXITY

Dipak Kr Das^†, Shashi Kant Mishra^‡, Pankaj Kumar^§, Savin Treanță^¶

Abstract: Integral inequalities based on generalized convexity are of great importance in both theoretical and applied mathematics. Due to its extensive applications, the study of integral inequalities has become one of the most rapidly advancing fields in mathematics. In this paper, we introduce several new classes of Milne-type inequalities using higher-order strongly exponentially convex functions. Novel relationships between various concepts of higher-order strongly exponentially functions are developed. These findings include several well-known results as well as some newly established results as particular cases. The results obtained in this paper can be viewed as a generalization and extension of previously known results.

Keywords: convex functions, exponentially convex functions, strongly exponentially convex functions, Milne type inequalities, Riemann-Liouville fractional integrals.

MSC: 35A01, 65L10, 65L12, 65L20, 65L70.

DOI 10.56082/annalsarscimath.2026.4.175

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^*Accepted for publication on July 29, 2026
^†dipakkrdas1995@bhu.ac.in, Department of Mathematics, Institute of Science, Banaras Hindu University, 221005 Varanasi, India
^‡shashikant.mishra@bhu.ac.in, Department of Mathematics, Institute of Science, Banaras Hindu University, 221005 Varanasi, India
^§p_mmv@bhu.ac.in, Department of Mathematics, Institute of Science, Banaras Hindu University, 221005 Varanasi, India
^¶savin.treanta@upb.ro, Department of Applied Mathematics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania; Academy of Romanian Scientists, 050044 Bucharest, Romania

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 4, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997