Stud. Univ. Babe¸ s-Bolyai Math. 68(2023), No. 2, 237–247 DOI: 10.24193/subbmath.2023.2.01 On a generalization of the Wirtinger inequality and some its applications Latifa Agamalieva, Yusif S. Gasimov and Juan E. N´apoles-Valdes Abstract. In this paper, we present generalized versions of the Wirtinger inequal- ity, which contains as particular cases many of the well-known versions of this classic isoperimetric inequality. Some applications and open problems are also presented in the work. Mathematics Subject Classification (2010): 26A33, 26Dxx, 35A23. Keywords: Integral operator, fractional calculus, Wirtinger inequality. 1. Introduction It is known that Fractional Calculus has a history practically similar to that of Ordinary Calculus, however only in the last 40 years has it become one of the most dynamic areas of Mathematics. Not only the development of the ”classic” (global to be more precise) Fractional Calculus has contributed to this, but since the 1960s generalized differential operators, called local fractional ones, began to appear, which have shown their usefulness in different problems of application. However, until 2014 (see [22]) it is that a formalization of these operators is not achieved with the appear- ance of what is called Conformable Derivative, on the other hand, in 2018, a local derivative of a new type is presented, called Non conformable [13, 34], which comes to consolidate this area as one in constant development. As we said, between the theoretical development and the multiplicity of applica- tions, a multitude of operators, fractional and generalized, have appeared, making it practically impossible to follow these new operators. In [5] suggests and justifies the idea of a fairly complete classification of the known operators of the Fractional Cal- culus (global or local), on the other hand, in the work [6] some reasons are presented Received 27 August 2020; Accepted 22 September 2020. Studia UBB MATHEMATICA. Published by Babe¸ s-Bolyai University This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.