Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative

Demonstratio mathematica

article

Mouffak Benchohra¹  Soufyane Bouriah³  Juan J. Nieto⁴ 

[1] Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes;Department of Mathematics, College of Science, King Saud University;Department of Mathematics Faculty of Exact Sciences and Informatics Hassiba Benbouali University;Instituto de Matemáticas, Universidade de Santiago de Compostela

关键词: Riemann-Liouville fractional derivative;    initial value problem;    existence;    uniqueness;    Ulam stability;    fixed point theorem;   

DOI  :  10.1515/dema-2019-0032

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results.

【 授权许可】

CC BY