HILFER AND HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS
IN FRECHET SPACESSA¨ID ABBAS, MOUFFAK BENCHOHRA, NAIMA HAMIDI AND JUAN J. NIETO
Abstract.In this paper, by using the fixed point theory and the technique relying on the
concept of measure of noncompactness in Fr´echet spaces, we prove some existence and Ulam–
Hyers–Rassias stability results for some Hilfer and Hilfer–Hadamard fractional differential equations.
Keywords: fractional differential equation, left-sided mixed integral, fractional order, Hilfer
fractional derivative, measure of noncompactness, Fr´echet space, existence, Ulam stability, fixed