Faiza, ChebabhaSupervisor: Nassim, FERAHTIA2025-07-072025-07-072025-06-15https://repository.univ-msila.dz/handle/123456789/46658In this dissertation, we studied the deformable and conformable Laplace transform, where we gave exact solutions of fractional differential equations with a fractional derivative called the deformable fractional derivative of order α, where 0 < α ≤ 1. Also we studied the conformable fractional Laplace transform of the fractional Chebyshev and Legendre polynomials.enLaplace transformDeformable fractional derivativeChebyshev polynomialsLegendre polynomialsThesis