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New results of the ρ-Jafari transform and their application to linear and nonlinear generalized fractional differential equations
Nuevos resultados de la transformada de ρ-Jafari y su aplicación a ecuaciones diferenciales fraccionarias generalizadas lineales y no lineales
DOI:
https://doi.org/10.15446/recolma.v58n1.117432Palabras clave:
Jafari transform, generalized fractional integral, Caputo generalized fractional derivative, exact solution (en)Transformada de Jafari, integral fraccionaria generalizada, derivada fraccionaria generalizada de Caputo, soluci´on exacta (es)
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Recently Hossein Jafari introduced a new general integral transform called Jafari transform to solve higher order initial value problems and integral equations. The main objective of this paper is to modify this integral transform that we call the ρ-Jafari transform and to study its properties. Then, we present interesting results and apply them to solve linear and nonlinear generalized fractional differential equations. The results obtained confirmed that the ρ-Jafari transform acts as a powerful tool for generalized fractional problems. As a result, we assert that in the future, the modified transform can be applied to many generalized fractional differential equations that arise in applied science and engineering.
Recientemente, Hossein Jafari introdujo una nueva transformada integral general llamada transformada de Jafari para resolver problemas de valores iniciales de orden superior y ecuaciones integrales. El principal objetivo de este trabajo es modificar esta transformada integral que llamamos transformada ρ-Jafari y estudiar sus propiedades. Luego, presentamos resultados interesantes y los aplicamos para resolver ecuaciones diferenciales fraccionarias generalizadas lineales y no lineales. Los resultados obtenidos confirmaron que la transformada ρ-Jafari actúa como una poderosa herramienta para problemas fraccionarios generalizados. Como resultado, afirmamos que en el futuro, la transformada modificada se podrá aplicar a muchas ecuaciones diferenciales fraccionarias generalizadas que surgen en las ciencias aplicadas y la ingeniería.
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