A Gronwall inequality with singularities
Resumen
An inequality of Gronwall type including singularities is derived. Its application to solve uniqueness problems is showed and a connection between this type of inequalities and the Mittag-Leffler functions is also proved.
Citas
Bateman, H.: Higher transcendental functions Volume III. McGraw-Hill Book Company Inc., New York (1955).
Johnston, I., Kolokoltsov, V.: Green’s function estimates for time-fractional evolution equations. Fractal and fractional 3, 36 (2019).
Kolokoltsov, V.: Differential Equations on Measures and Functional Spaces. Birkhäuser Advanced Texts Basler Lehrbücher, e-book (2019).
Mainardi, F., Gorenflo, R.: On Mittag-Leffler-type functions in fractional evolution processes. Journal of Computational and Applied Mathematics 118, 283-299 (2000).
Mathai, A.M., Saxena, R.K., Haubold, H.J.: The H-Function Theory and Applications. Springer, New York (2010).
Solís, S., Vergara, V.: A non-linear stable non-Gaussian process in fractional time. Topol. Methods Nonlinear Anal. 59, 987–1028 (2022).
Solís, S., Vergara, V.: Blow-up for a non-linear stable non-Gaussian process in fractional time. Fractional Calculus and Applied Analysis 26, 1206–1237 (2023).
Uchaikin, V., Zolotarev, V.: Chance and stability: stable distributions and their applications. Monographs Modern Probability and Statistics, Moscow (1999).
Ye, H., Gao, J., Ding, Y.: A generalized Gronwall inequality and its application to a fractional differential equation. J. Math. Anal. Appl. 328, 1075–1081 (2007).
Johnston, I., Kolokoltsov, V.: Green’s function estimates for time-fractional evolution equations. Fractal and fractional 3, 36 (2019).
Kolokoltsov, V.: Differential Equations on Measures and Functional Spaces. Birkhäuser Advanced Texts Basler Lehrbücher, e-book (2019).
Mainardi, F., Gorenflo, R.: On Mittag-Leffler-type functions in fractional evolution processes. Journal of Computational and Applied Mathematics 118, 283-299 (2000).
Mathai, A.M., Saxena, R.K., Haubold, H.J.: The H-Function Theory and Applications. Springer, New York (2010).
Solís, S., Vergara, V.: A non-linear stable non-Gaussian process in fractional time. Topol. Methods Nonlinear Anal. 59, 987–1028 (2022).
Solís, S., Vergara, V.: Blow-up for a non-linear stable non-Gaussian process in fractional time. Fractional Calculus and Applied Analysis 26, 1206–1237 (2023).
Uchaikin, V., Zolotarev, V.: Chance and stability: stable distributions and their applications. Monographs Modern Probability and Statistics, Moscow (1999).
Ye, H., Gao, J., Ding, Y.: A generalized Gronwall inequality and its application to a fractional differential equation. J. Math. Anal. Appl. 328, 1075–1081 (2007).
