%0 Journal Article %T Existence and stability results for Hilfer-Katugampola-type fractional implicit differential equations with nonlocal conditions %A Salamooni, Ahmad Y. A. %A Pawar, D. D. %J Journal of Nonlinear Sciences and Applications %D 2021 %V 14 %N 3 %@ ISSN 2008-1901 %F Salamooni2021 %X This article contains a new discussion for Hilfer-Katugampola-type fractional derivative. We establish an existence and uniqueness results of Hilfer-Katugampola-type fractional derivative for implicit differential equations with the help of Schaefer's fixed point theorem and Banach contraction principle. Also, we use the Gronwall's lemma for singular kernels to prove the Ulam-Hyers-Rassias stability results. Further, the examples are given to illustrate our main results. %9 journal article %R 10.22436/jnsa.014.03.02 %U http://dx.doi.org/10.22436/jnsa.014.03.02 %P 124--138