Fractional integral operators play an important role in generalizations and extensions of various subjects of sciences and engineering. This research is the study of bounds of Riemann-Liouville fractional integrals via (h − m)-convex functions. The author succeeded to find upper bounds of the sum of left and right fractional integrals for (h − m)-convex function as well as for functions which are deducible from aforementioned function (as comprise in Remark 1.2). By using (h − m) convexity of |f ′ | a modulus inequality is established for bounds of Riemann-Liouville fractional integrals. Moreover, a Hadamard type inequality is obtained by imposing an additional condition. Several special cases of the results of this research are identified.
Farid, G. (2021). Bounds of Riemann-Liouville fractional integral operators. Computational Methods for Differential Equations, 9(2), 637-648. doi: 10.22034/cmde.2020.32653.1516
MLA
Ghulam Farid. "Bounds of Riemann-Liouville fractional integral operators". Computational Methods for Differential Equations, 9, 2, 2021, 637-648. doi: 10.22034/cmde.2020.32653.1516
HARVARD
Farid, G. (2021). 'Bounds of Riemann-Liouville fractional integral operators', Computational Methods for Differential Equations, 9(2), pp. 637-648. doi: 10.22034/cmde.2020.32653.1516
VANCOUVER
Farid, G. Bounds of Riemann-Liouville fractional integral operators. Computational Methods for Differential Equations, 2021; 9(2): 637-648. doi: 10.22034/cmde.2020.32653.1516
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