On conformable double Laplace transform Ozan Özkan 1 · Ali Kurt 2 Received: 11 September 2017 / Accepted: 30 January 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this study authors introduce the conformable double Laplace transform which can be used to solve fractional partial differential equations that represents many physical and engineering models. In these models the derivatives and integrals are in the sense of newly defined conformable type. Then some properties of conformable double Laplace transform are expressed. Finally fractional heat equation and fractional telegraph equation which is used in various applications in science and engineering investigated as an application of this new transform. Keywords Double Laplace transform · Conformable fractional derivative · Conformable fractional integral · Fractional heat equation · Fractional telegraph equation Mathematics Subject Classification 35R11 · 35A20 · 35C05 1 Introduction The topic of partial differential equations attracts huge amount of scientists for many years. So it has become the most important subject for a lot of sciences such as mathematics, physics, engineering. Due to this importance scientists have been studying to obtain the numerical or analytical solutions of the mathematical models arising in these areas. Because all the scientists know that obtaining the solutions of these models means understanding the complexity of nature. All the story of humankind depends on this aim, & Ali Kurt alikurt@mku.edu.tr Ozan Özkan oozkan@selcuk.edu.tr 1 Department of Mathematics, Selc¸uk University, Konya, Tu¨rkiye 2 Department of Mathematics, Mustafa Kemal University, Hatay, Tu¨rkiye 123 Opt Quant Electron (2018)50:103 https://doi.org/10.1007/s11082-018-1372-9