%0 Journal Article %T New approach to existence of solution for weighted Cauchy-type problem %J Journal of Mathematical Modeling %I University of Guilan %Z 2345-394X %A Bhairat, Sandeep P. %D 2020 %\ 09/01/2020 %V 8 %N 4 %P 377-391 %! New approach to existence of solution for weighted Cauchy-type problem %K Fractional integrals and derivatives %K Picard iterative technique %K singular fractional differential equation %K Cauchy-type problem %R 10.22124/jmm.2020.14983.1393 %X In this paper, we consider a singular differential equation involving Hilfer-Katugampola fractional derivative with the weighted initial condition. The Picard iterative technique has been successfully applied to obtain the existence of a unique solution. First, we derive an equivalent integral equation, then construct the successive approximations and use the ratio test to discuss its convergence. We demonstrate our results through a suitable illustrative example. %U https://jmm.guilan.ac.ir/article_4063_06b6f9bdc9843bccefec98274fee504b.pdf