Caputo fractional derivative inequalities via $(h-m)$-convexity

Authors

  • Ghulam Farid COMSATS University Islamabad, Attock Campus Attock, Pakistan
  • Vishnu Narayan Mishra Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India

Abstract

The aim of this study is to establish some new Caputo fractional integral inequalities. By applying definition of $(h-m)$-convexity and some straightforward inequalities an upper bound of the sum of left and right sided Caputo fractional derivatives has been established. Furthermore, a modulus inequality and a Hadamard type inequality have been analyzed. These results provide various fractional inequalities for all particular functions deducible from $(h-m)$-convexity, see Remark \ref{rem1}.

Author Biography

Vishnu Narayan Mishra, Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India

Dr. Vishnu Narayan MishraAssociate Professor of Mathematics,Department of Mathematics,Indira Gandhi National Tribal University,Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India

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Published

2020-06-23

Issue

Vol. 16

Section

Vol. 16, No. 5, (2022)

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