PUBLICACIONES

EXISTENCIA Y UNICIDAD DE SOLUCIÓN PARA UNA ECUACIÓN DIFERENCIAL CON DERIVADA FRACCIONARIA DE MEMORIA FIJA

By: Jesús Avalos R.

Institution: Universidad Nacional de Trujillo - FCFyM

https://dspace.unitru.edu.pe/items/f46761ce-bf17-467a-a64f-f19f0ec99679

Abstract

The main objective of this thesis is to determine the sufficient conditions for the exis- tence and uniqueness of solution of a fractional differential equation with fixed memory length given by

 t−LDtαu(t) = f(t,u(t)), 0 < t ≤ T u|[−L,0] = 0

(P)

whereα∈(0,1),L>0,T >0andf :[0,T]×R→Risacontinuousfunction. For this, some fundamental properties of the fractional integral and the derivative with fixed-length memory are studied and thus establish an equivalence between the fractio- nal differential equation with fixed-length memory and a fractional integral equation, and then apply Banach’s fixed point theorem. on a space of adequate size. functions In addi- tion, the principle of short memory is studied and the Laplace transform of the integral and fractional derivative with fixed memory length is presented for the first time.

Key Words: Fractional calculus, fractional integral with fixed memory length, frac- tional derivative with fixed memory length, Laplace transform, Cauchy problem, fractio- nal differential equations.

Existência e Unicidade das Equações Diferenciais Fracionárias 

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By: Jesús P. Avalos Rodríguez.

Institution: Universidade Federal de Goiás- IME.

Abstract:

This work has the main objective to study the conditions of existence and uniqueness of linear and non linear fractional differential equations, and analysis of a system of fractional differential equations. For this purpose, basic theory of fractional calculus is shown, with the Riemann-Liouville fractional integral and Riemann- Liouville fractional derivative.

Una Generalización de la Integral y Derivada de orden entero a orden arbitrario. 

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By: Jesús Avalos R.

Institution: Universidad Nacional de Trujillo - FCFyM

Resumen:

El presente trabajo proporciona una visión general del cálculo fraccionario, en las cuales se desarrolla las diversas aproximaciones de la integral fraccionaria, sus principales propiedades; así como proponer una interpretación física y geométrica de la integral y derivada de orden fraccionario.