This article is aimed at establishing some results concerning integral inequalities of the Opial ... more This article is aimed at establishing some results concerning integral inequalities of the Opial type in the fractional calculus scenario. Specifically, a generalized definition of a fractional integral operator is introduced from a new Raina-type special function, and with certain results proposed in previous publications and the choice of the parameters involved, the established results in the work are obtained. In addition, some criteria are established to obtain the aforementioned inequalities based on other integral operators. Finally, a more generalized definition is suggested, with which interesting results can be obtained in the field of fractional integral inequalities.
Revista de Matemática: Teoría y Aplicaciones, 2009
The problem of convergence, as t → +∞, of solutions of the system (1) is considered. It is assume... more The problem of convergence, as t → +∞, of solutions of the system (1) is considered. It is assumed that the functions α, f and g are of class C1 for all values of their arguments, furthermore g′(x) > 0, f ′(x) ≥ r > 0, 0 < n ≤ α′(y) ≤ N < +∞ and the functions a(t) and p(t) are continuous on [0, +∞) with 0 < a ≤ a(t) ≤ A < +∞ and p(t) ≥ 0.
This article is aimed at establishing some results concerning integral inequalities of the Opial ... more This article is aimed at establishing some results concerning integral inequalities of the Opial type in the fractional calculus scenario. Specifically, a generalized definition of a fractional integral operator is introduced from a new Raina-type special function, and with certain results proposed in previous publications and the choice of the parameters involved, the established results in the work are obtained. In addition, some criteria are established to obtain the aforementioned inequalities based on other integral operators. Finally, a more generalized definition is suggested, with which interesting results can be obtained in the field of fractional integral inequalities.
Revista de Matemática: Teoría y Aplicaciones, 2009
The problem of convergence, as t → +∞, of solutions of the system (1) is considered. It is assume... more The problem of convergence, as t → +∞, of solutions of the system (1) is considered. It is assumed that the functions α, f and g are of class C1 for all values of their arguments, furthermore g′(x) > 0, f ′(x) ≥ r > 0, 0 < n ≤ α′(y) ≤ N < +∞ and the functions a(t) and p(t) are continuous on [0, +∞) with 0 < a ≤ a(t) ≤ A < +∞ and p(t) ≥ 0.
Uploads
Papers by Juan Nápoles