Conference submissions

Exploring the exact differential equations with GeoGebra software

Jorge Olivares Funes1 , Elvis Valero2

1University of Antofagasta, Department of Mathematics, Chile
2Universidad de Tarapacá, matemáticas, Chile

Abstract

In this paper, we will show the solutions of certain exact differential equations that are obtained through the interactive GeoGebra software. GeoGebra software has been of great motivational support in the processes of teaching and modeling in mathematics in various universities and colleges, especially in the engineering careers of the University of Antofagasta in the courses of differential equations and calculation of several variables.


The modified functions of Bessel I_3/4(x) and I_-3/4(x) in certain fractional differential equations

Jorge Olivares Funes1 , Pablo Martin2 , Elvis Valero3

1University of Antofagasta, Department of Mathematics, Chile
2University of Antofagasta, physics department, Chile
3Universidad de Tarapacá, matemáticas, Chile

Abstract

The fractional derivative of Caputo, has huge and important applications in various areas of science and engineering. In this case, through the definition of the Caputo derivative and the Laplace transform and its inverse, we propose to show the various hypergeometric solutions that can be obtained for each specific value of m of the following fractional differential equations d^m y/dx^m= I_3/4(x) , y(0)=0, 0< m<1 and d^m y/dx^m= I_-3/4(x) , y(0)=0, 1< m<2. Where the non-homogeneous parts I_3/4(x) and I_-3/4(x) are the modified Bessel functions of the first species.


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Dimitrios Vlachos1

1University of Peloponnese, Department of Informatics and Telecommunications, Greece

Abstract

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