Abstract
Integral inequalities are considered to be important as they have many applications described by a number of researchers. Moreover, the theory of fractional calculus is used in solving differential, integral, and integro-differential equations and also in various other problems involving special functions. In this research article, we present the improved version of generalizations for a Gruss type integral inequality by taking a generalized Riemann-Liouville fractional integral in terms of a new parameter $k>0$ . We contribute in the on going research by providing mathematical results that can be verified easily.
Highlights
1 Introduction Since the integral inequalities are considered to be important, the research has been proceeded to extend the investigation for such type of inequalities
Such inequalities and its applications are extensively described in many articles
1.2 Related work Researchers focused in investigating such integrals and provided remarkable results for inequalities involving Riemann-Liouville fractional integrals like the Grüss, Chebyshev and Hermite-Hadamard type inequalities for integrable functions as well as for convex functions
Summary
Since the integral inequalities are considered to be important, the research has been proceeded to extend the investigation for such type of inequalities. Riemann-Liouville fractional integral of order α ≥ is defined by Definition If f ∈ L ,r[a, b], the generalized Riemann-Liouville fractional integral Iaα,r of order α ≥ and r ≥ , introduced by is defined by 1.2 Related work Researchers focused in investigating such integrals and provided remarkable results for inequalities involving Riemann-Liouville fractional integrals like the Grüss, Chebyshev and Hermite-Hadamard type inequalities for integrable functions as well as for convex functions (see [ – ]).
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