Khalid, MohdAkgul, Ali2024-12-242024-12-2420242705-10642705-1056https://doi.org/10.37256/cm.5320244620https://hdl.handle.net/20.500.12604/8332The Formable integral transform for the Hilfer-Prabhakar and Prabhakar fractional derivatives, as well as their regularised forms, are derived in this article. We solve several Cauchy-type fractional differential equations with Hilfer-Prabhakar fractional derivatives by applying the Formable integral and Fourier transformations in their entirety, including the three-parameter Mittag-Leffler function. With the help of analytical solutions and improved comprehension of complicated fractional differential equations, this work expands the use of integral transforms in fractional calculus across a range of scientific and engineering fields.eninfo:eu-repo/semantics/openAccessPrabhakar integralHilfer-Prabhakar derivativesformable transformFourier transformMittag-Leffler functionArticle5326932708N/AWOS:001288459000007Q42-s2.0-8520154528110.37256/cm.5320244620