On fractional order derivatives and Darboux problem for implicit differential equations

By Saïd Abbas, Mouffak Benchohra, A. Vityuk. Fractional Calculus and Applied Analysis, 2012

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In this paper we prove some relations between the Riemann-Liouville and the Caputo fractional order derivatives, and we investigate the existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of functional hyperbolic differential equations by using some fixed point theorems.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0de140db3864eaddb6f520425d585e11af380cae