DNA Vibration Amplitudes with Generalized Potentials and Matlab-Positive Solutions

Objective: We analyse the existence and uniqueness of the positive solutions of a coupled system of second-order boundary-valued differential equations, which the boundary conditions are coupled by integrals. For that one, the solutions are related to integral equations. Method: Unilateral Fourier transform and Compression and expansion fixed point theorem. Results and Discussion: We analyzed the amplitude and the velocity of waves of DNA breathing for another Morse potentials. The importance of DNA dynamics with generalized potentials dependent on a parameter lies in the results obtained being equal to DNA dynamics with fractional order derivatives. Likewise, in an analytical and computational way, estimates of the amplitude of DNA vibrations with generalized potentials are obtained, whether they are symmetrical Morse potentials or also for Morse potentials dependent on a parameter in their exponential expression. Implications of the research: Apply in the first university years the application of MATLAB-GEOGEBRA to discrete dynamic systems in all university careers and specialties as part of the management of the tools of Information and Communication Technology (TIC). Originality/Value: This paper also provides an alternative approach to Analysis of dna vibration amplitudes with generalized potentials.