Khalid, MohdMallah, Ishfaq AhmadAkgul, AliAlha, SubhashSakar, Necibullah2024-12-242024-12-2420242238-36031807-0302https://doi.org/10.1007/s40314-024-02930-0https://hdl.handle.net/20.500.12604/6256This paper introduces the Psi-formable integral transform, discusses the several essential properties and results-Convolution, Psi-formable transform of tth derivative, Psi-Riemann Liouville fractional integration and differentiation, Psi-Caputo fractional differentiation, Psi-Hilfer fractional differentiation, Psi-Prabhakar fractional integration and differentiation, and Psi-Hilfer-Prabhakar fractional derivatives. Next, we use the Fourier integral and Psi-Modifiable conversions to solve some Cauchy-type fractional differential equations using the generalized three-parameter Mittag-Leffler function and Psi-Hilfer-Prabhakar fractional derivativeseninfo:eu-repo/semantics/closedAccessPsi-Prabhakar integralPsi-Formable transformPsi-Hilfer Prabhakar derivativesMittag-Leffler functionArticle437N/AWOS:001314718700003Q12-s2.0-8520430222910.1007/s40314-024-02930-0