Abstract
This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences.
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Details
1 National Higher School of Technology and Engineering, Department CPST, Annaba, Algeria
2 Düzce University, Department of Mathematics, Faculty of Science and Arts, Düzce, Turkey (GRID:grid.412121.5) (ISNI:0000 0001 1710 3792)
3 Government College University, Department of Mathematics, Faisalabad, Pakistan (GRID:grid.411786.d) (ISNI:0000 0004 0637 891X)
4 University of 8 May 1945 Guelma, Laboratory of Analysis and Control of Differential Equations “ACED”, Facuty MISM, Department of Mathematics, Guelma, Algeria (GRID:grid.411786.d)