Newly Defined Conformable Double Laplace Transform and Partial Differential Equations with Conformable Derivative - Labade, M. B.; Gavhane, B. D.; Gaikwad, S. B. (Communications in Mathematics and Applications, 2025)
This study provides a comprehensive investigation of the newly defined conformable double Laplace transform and the conformable derivatives. Several distinct properties of the conformable double Laplace transform are explored. The effectiveness and reliability of the method are demonstrated by obtaining analytical solutions to initial and boundary value problems associated with well-known fractional partial differential equations involving conformable derivatives.
Keywords: Conformable derivative; Conformable integral; Conformable double Laplace transform; Conformable partial differential equations; Klein-Gordan equation; Kdv equation