In 2014 Khalil et al. introduced a new definition of a local fractional derivative the Khalil's derivative from integer order calculus as a simple change of variable. Simultaneously from 2014 others conformable derivatives have emerged. All these derivatives depend on a particular kernel. In this article we study what properties the kernels can have in order for such conformable derivatives to be interpreted from the integer order calculus making a change of variable. In other hand, in 2018 other local fractional derivative called non-conformable (NCFD) was presented. Regarding this last derivative, new theoretical studies have appeared that allow an even greater generalization of fractional derivates. We demonstrate that the NCFD can also be interpreted from the integer order calculus by making a change of variable. In summary, in this paper we give necessary conditions on the respective kernels so that both derivatives can be reinterpreted from integer-order calculus.
Climate change is a determining factor in the development of negative environmental impacts. Identifying its contributing factors within the Latin American context takes on a heightened importance, and it is here that statistical methods help to make inferences. In Latin America, where ecological complexities abound, the emission profile is influenced by different activities, such as significant land use changes and agricultural activities. Therefore, this academic pursuit focuses on a meticulous study of variables that include energy consumption, land use, methane, nitrous oxide, and CO2 emissions from oil. In order to fully grasp the complex relationship between these variables and the countries under consideration, the HJ-Biplot methodology is used to extract information by interpreting the graphs presented. In this context, it was found that the Central American countries make a relatively modest contribution, while the experiences of Paraguay and Brazil underscore the robust relationship between environmental policies and the impact of climate change.
In this paper we study the well-known Hermite-Hadamard inequality for (h, m)-convex functions of the first and second type using weight Caputo derivatives of the right-hand side and the left-hand side of order alpha.
The detection of discontinuities of a function f (x, y) is the first step in problems of approximation of surfaces with strong variations (non-regular or discontinuous functions). This situation can be found in an important number of applications in concrete situations, such as modeling in Geology, and the reconstruction of medical or satellite images, among others. The purpose of this work is to present a methodology to detect and cover the set of discontinuities in explicit non-regular functions, from a set of N sparse Lagrangian data, (xi(j), f (xi(j))), with j is an element of {1, 2,.. . , N}, coming from a function explicitly defined as z = f (x, y). The proposed approach consists of the detection and approximation of a discontinuity set, and then the construction of a covering over that set. Results are presented for the detection and covering of polygonal curves derived from vertical faults present in discontinuous surfaces, using a scattered dataset of Lagrange type as input information. As a conclusion we obtain that the proposed methodology will open a way to define non-regular functional spaces, flexible enough to be adapted to the necessary requirements for the approximation of discontinuous surfaces.
Phenomena such as the movement of fermionic particles of spin 3/2, such as the Delta Baryons, Gravitino and the Graviton, are of great interest. Given their spins, these particles follow the movement described by the Rarita-Schwinger equation, making their study crucial. Many mathematicians and physicists have contributed to the development of this theory, as noted in [1], however, recent works, such as [2] which study the weighted Dirac operator, have laid the groundwork for new studies on the motion of spin particles 3/2, such as this study of the weighted Rarita-Schwinger operator and its fundamental solution that theoretically describes the motion of these particles in anisotropic media. This work presents the solution of the RaritaSchwinger operator in parameter-dependent Clifford algebra. In a first part, the Rarita Schwinger operator was defined using the weighted Dirac operator and the weighted Euler and Gamma operators, then the space of the weighted monogenic functions and a basis that describes it was found, a space to which the fundamental solution belongs, the fundamental solution was obtained using the methodology from [3].
