Certain Grüss-type inequalities via tempered fractional integrals concerning another function. (English) Zbl 1503.26073
Summary: We study a generalized left sided tempered fractional (GTF)-integral concerning another function \(\Psi\) in the kernel. Then we investigate several kinds of inequalities such as Grüss-type and certain other related inequalities by utilizing the GTF-integral. Additionally, we present various special cases of the main result. By utilizing the connection between GTF-integral and Riemann-Liouville integral concerning another function \(\Psi\) in the kernel, certain distinct particular cases of the main result are also presented. Furthermore, certain other inequalities can be formed by applying various kinds of conditions on the function \(\Psi \).
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26A33 | Fractional derivatives and integrals |
| 34A08 | Fractional ordinary differential equations |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
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