Karatas Akgül, EsraAkgül, Ali2024-12-242024-12-2420222349-5103https://doi.org10.1007/s40819-022-01452-9https://hdl.handle.net/20.500.12604/4014Caputo fractional derivative and Riemann–Liouville integral are very helpful operators to model non-local behaviours. Then by using these operators, investigators defined a new operator that is the proportional derivative. In some cases, this operator can be written like a linear combination of a Riemann–Liouville integral and a Caputo derivative. In this study, we used Caputo derivative and constant proportional Caputo derivative when solving our examples with Sumudu transform method. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.eninfo:eu-repo/semantics/closedAccessFractional derivativePower-law kernelProportional derivativeSumudu transformsArticle85Q22-s2.0-8513721727510.1007/s40819-022-01452-9