Bounds of Riemann-Liouville fractional integral operators

	Bounds of Riemann-Liouville fractional integral operators
Computational Methods for Differential Equations
مقاله 20، دوره 9، شماره 2، تیر 2021، صفحه 637-648 اصل مقاله (127.88 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.32653.1516
نویسنده
Ghulam Farid^*
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan.
چکیده
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.
کلیدواژه‌ها
Convex function؛ (h − m)-convex function؛ Riemann-Liouville fractional integral operators؛ Bounds

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