Integral inequalities for several strongly convex functions including Caputo-Fabrizio fractional integral operators

L'Hospital's question to Leibniz concerning the existence of fractional-order derivatives marked the beginning of fractional calculus, yet research in this area remained limited for nearly fifty years. Over time, its innovative approach to modeling non-local problems and its applicability to complex real-world challenges significantly accelerated developments in the field. Consequently, fractional calculus has become a prominent area of study within mathematics, physics, engineering, economics, biology, and various other science and engineering disciplines. Recently, the combined study of fractional derivatives, integrals, and inequality theory has yielded important findings, demonstrating that more general forms of existing integral inequalities can be established. This thesis focuses on the integral definitions corresponding to the non-singular fractional derivative introduced by M. Caputo and M. Fabrizio in 2015. New Hermite Hadamard and Ostrowski type inequalities are derived using Caputo–Fabrizio fractional integrals for certain classes of strongly convex functions.