AbstractIn this paper, we use some fixed point theorems in Banach space for studying the existence and uniqueness results for Hilfer–Hadamard-type fractional differential equations $$ {}_{\mathrm{H}}D^{\alpha ,\beta }x(t)+f\bigl(t,x(t)\bigr)=0 $$
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on the interval $(1,e]$
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with nonlinear boundary conditions $$ x(1+\epsilon )=\sum_{i=1}^{n-2}\nu _{i}x(\zeta _{i}),\qquad {}_{\mathrm{H}}D^{1,1}x(e)= \sum_{i=1}^{n-2} \sigma _{i}\, {}_{\mathrm{H}}D^{1,1}x( \zeta _{i}). $$
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Existence and uniqueness results for the coupled systems of implicit fractional differential equations with periodic boundary conditions
