FRACTIONAL INTEGRAL INEQUALITIES OF OSTROWSKI AND HADAMARD TYPE VIA k-ANALOGUES OF CAPUTO DERIVATIVES

Yonghong Liu, Ghulam Farid, Loay Alkhalifa and Waqas Nazeer
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Yonghong Liu: School of Computer Science, Chengdu University, Chengdu 610106, P. R. China
Ghulam Farid: ��Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
Loay Alkhalifa: ��Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Waqas Nazeer: �Department of Mathematics, Government College University Lahore, Pakistan

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-11

Abstract: Fractional derivative operators are important tools for generalizing concepts and theories based on usual derivatives and integrals. Many integral and derivative inequalities in the literature can be analyzed for fractional integrals and derivatives. In this paper, well-known Ostrowski and Hadamard integral inequalities are established by using fractional derivatives. These inequalities estimate the bounds of k-analogues of Caputo fractional derivatives (CFk-D). An Ostrowski–Grüss-type inequality is also established under new constraints. Applications of these inequalities are given at fixed points, and various already published results are obtained.

Keywords: Ostrowski Inequality; Hadamard Inequality; Ostrowski–Grüss Inequality; Caputo Fractional Derivatives (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400729

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