Sobre operadores Riemann-Liouville de tipo (α, k, P) y espacios de funciones asociados
DOI:
https://doi.org/10.19136/jobs.a12n34.6686Palabras clave:
Integral fraccional, derivada fraccional, k-operadores de tipo Riemann-Liouville, (α, k, P)-operadores de tipo Riemann-Liouville, espacios de funciones, elección de trayectorias, funciones de longitud de arcoResumen
En este trabajo se llevó a cabo una primera investigación sobre las integrales y diferenciales de Riemann-Liouville de tipo (α, k, P). Se obtuvo una generalización de los operadores k fraccionarios para funciones de una variable planteados en trabajos previos, en conjunto los con operadores fraccionarios de trayectoria para funciones de varias variables recientemente propuestos. Se definieron los espacios de funciones relevantes asociados a dichos operadores y se exploraron primeras propiedades sobre los mismos. Asimismo, se proporcionaron ejemplos de derivadas e integrales fraccionarias conocidas que resultan como casos particulares y finalmente, se complementó el estudio con los teoremas fundamentales del c´alculo correspondientes a estos operadores
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