Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities
Muhammad Bilal Khan,
Hatim Ghazi Zaini,
Savin Treanțǎ,
Gustavo Santos-García,
Jorge E. Macías-Díaz,
Mohamed S. Soliman
Affiliations
Muhammad Bilal Khan
Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
Hatim Ghazi Zaini
Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Savin Treanțǎ
Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Gustavo Santos-García
Facultad de Economía y Empresa and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, Spain
Jorge E. Macías-Díaz
Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico
Mohamed S. Soliman
Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
In this paper, we discuss the Riemann–Liouville fractional integral operator for left and right convex interval-valued functions (left and right convex I∙V-F), as well as various related notions and concepts. First, the authors used the Riemann–Liouville fractional integral to prove Hermite–Hadamard type (𝓗–𝓗 type) inequality. Furthermore, 𝓗–𝓗 type inequalities for the product of two left and right convex I∙V-Fs have been established. Finally, for left and right convex I∙V-Fs, we found the Riemann–Liouville fractional integral Hermite–Hadamard type inequality (𝓗–𝓗 Fejér type inequality). The findings of this research show that this methodology may be applied directly and is computationally simple and precise.
