An Extension of the Fractional Gronwall Inequality
In this work, we prove a generalization of the Gronwall type inequality. This relation can be used in the qualitative analysis of the solutions to fractional differential equations with the \(\psi \)-fractional derivatives.
KeywordsFractional operators Gronwall type inequality
R. Almeida is supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UID/MAT/04106/2019. A. B. Malinowska is supported by the Bialystok University of Technology grant S/WI/1/2016 and T. Odzijewicz by the Warsaw School of Economics grant KAE/S18/08/18.
- 14.Qian, D., Gong, Z., Li, C.: A generalized Gronwall inequality and its application to fractional differential equations with Hadamard derivatives. In: Proceedings of the 3rd Conference on Nonlinear Science and Complexity, Cankaya University (2010)Google Scholar