Jorge Olivares Funes^{1}
, Elvis Valero^{2}

^{1}University of Antofagasta, Department of Mathematics, Chile

^{2}Universidad de Tarapacá, matemáticas, Chile

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.

Jorge Olivares Funes^{1}
, Pablo Martin^{2}
, Elvis Valero^{3}

^{1}University of Antofagasta, Department of Mathematics, Chile

^{2}University of Antofagasta, physics department, Chile

^{3}Universidad de Tarapacá, matemáticas, Chile

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.

Dimitrios Vlachos^{1}

^{1}University of Peloponnese, Department of Informatics and Telecommunications, Greece

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