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.
Bhairat, S. P. (2020). New approach to existence of solution for weighted Cauchy-type problem. Journal of Mathematical Modeling, 8(4), 377-391. doi: 10.22124/jmm.2020.14983.1393
MLA
Sandeep P. Bhairat. "New approach to existence of solution for weighted Cauchy-type problem". Journal of Mathematical Modeling, 8, 4, 2020, 377-391. doi: 10.22124/jmm.2020.14983.1393
HARVARD
Bhairat, S. P. (2020). 'New approach to existence of solution for weighted Cauchy-type problem', Journal of Mathematical Modeling, 8(4), pp. 377-391. doi: 10.22124/jmm.2020.14983.1393
VANCOUVER
Bhairat, S. P. New approach to existence of solution for weighted Cauchy-type problem. Journal of Mathematical Modeling, 2020; 8(4): 377-391. doi: 10.22124/jmm.2020.14983.1393
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