In this paper, new analytical solutions for a class of conformable fractional differential equations (CFDEs) and some more results about Laplace transform introduced by Abdeljawad are investigated. The Laplace transform method is developed to get the exact solution of CFDEs. The aim of this paper is to convert the CFDEs into ordinary differential equations (ODEs), this is done by using the fractional Laplace transform of (α + β) order.
 T. Abdeljawad, On conformable fractional calculus, Journal of computational and Applied Mathematics, 279 (2015), 57–66.
 Z. Al-Zhour, N. Al-Mutairi, F. Alrawajeh, and R. Alkhasawneh, New theoretical results and applications on conformable fractional Natural transform, Ain Shams Engineering Journal, Elsevier, 2020.
 A. Atangana and I. Koca, Chaos in a simple nonlinear system with atangana–baleanu derivatives with fractional order, Chaos, Solitons & Fractals, 89 (2016), 447–454.
 A. Atangana, D. Baleanu, and A. Alsaedi, New properties of conformable derivative, Open Mathematics, 13(1) (2015).
 D. Baleanu, A. Jajarmi, and JH. Asad, The fractional model of spring pendulum: New features within different kernels, 2018.
 D. Baleanu, S. S. Sajjadi, A. Jajarmi, and J. H. Asad, New features of the fractional euler-lagrange equations for a physical system within non-singular derivative operator, The European Physical Journal Plus, 134(4) (2019), 181.
 M. Caputo, and M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl, 1(2) (2015), 1–13.
 YÜ. Cenesiz and A. Kurt, The solution of time fractional heat equation with new fractional derivative definition, in: 8th International Conference on Applied Mathematics, Simulation, Modelling, 195 (2014).
 Y. Çenesiz, D. Baleanu, A. Kurt, and O. Tasbozan, New exact solutions of burgers type equations with conformable derivative, Waves in Random and complex Media, 27(1) (2017), 103–116.
 Y. Edrisi-Tabriz, M. Lakestani, and M. Razzaghi, Study of B-spline collocation method for solving fractional op- timal control problems, Transactions of the Institute of Measurement and Control, Publisher, SAGE Publications Sage UK: London, England, (2021), pages, 0142331220987537.
 M. Ekici, M. Mirzazadeh, M. Eslami, Q. Zhou, S. P. Moshokoa, A. Biswas, and M. Belic, Optical soliton pertur- bation with fractional-temporal evolution by first integral method with conformable fractional derivatives, Optik, 127(22) (2016), 10659–10669.
 MS. Hashemi, Invariant subspaces admitted by fractional differential equations with conformable derivatives, Chaos, Solitons & Fractals, 107 (2018), 161–169.
 S. He, K. Sun, X. Mei, B. Yan, and S. Xu, Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative, The European Physical Journal Plus, 132(1) (2017), 1–11.
 R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264 (2014), 65–70.
 A. B. Mingarelli, On generalized and fractional derivatives and their applications to classical mechanics, Journal of Physics A: Mathematical and Theoretical, 51(36) (2018), 365204.
 H. Mortazaasl and A. A. Jodayree Akbarfam, Two classes of conformable fractional Sturm-Liouville problems: Theory and applications, Mathematical Methods in the Applied Sciences, Wiley Online Library, 44(1) (2021), 166–195.
 Z. Odibat, Fractional power series solutions of fractional differential equations by using generalized Taylor series, Applied and Computational Mathematics, Azerbaycan Dovlet Iqtisad Universiteti, 19(1) (2020), 47–58.
 K. Oldham and J. Spanier, The fractional calculus theory and applications of differentiation and integration to arbitrary order, Elsevier, 1974.
 M. D. Ortigueira, and J.A. Tenreiro Machado, What is a fractional derivative?, Journal of computational Physics, Elsevier, 293 (2015), 4–13.
 I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier, 1998.
 M. Pourbabaee and A. Saadatmandi, Collocation method based on Chebyshev polynomials for solving distributed order fractional differential equations, Computational Methods for Differential Equations, 9(3) (2020), 858-873.
 F. Shariffar, AH. Refahi Sheikhani, and M. Mashoof, Numerical Analysis of Fractional Differential Equation by TSI-Wavelet Method, Computational Methods for Differential Equations, 9(3) (2020), 659-669.
 NH. Sweilam, AM. Nagy, and AA. El-Sayed, Sinc-Chebyshev collocation method for time-fractional order telegraph equation, Appl. Comput. Math, 19(2) (2020), 162–174.
Molaei, M., Dastmalchi Saei, F., Javidi, M., Mahmoudi, Y. (2022). New analytical methods for solving a class of conformable fractional differential equations by fractional Laplace transform. Computational Methods for Differential Equations, 10(2), 396-407. doi: 10.22034/cmde.2021.40834.1775
Mohammad Molaei; Farhad Dastmalchi Saei; Mohammad Javidi; Yaghoub Mahmoudi. "New analytical methods for solving a class of conformable fractional differential equations by fractional Laplace transform". Computational Methods for Differential Equations, 10, 2, 2022, 396-407. doi: 10.22034/cmde.2021.40834.1775
Molaei, M., Dastmalchi Saei, F., Javidi, M., Mahmoudi, Y. (2022). 'New analytical methods for solving a class of conformable fractional differential equations by fractional Laplace transform', Computational Methods for Differential Equations, 10(2), pp. 396-407. doi: 10.22034/cmde.2021.40834.1775
Molaei, M., Dastmalchi Saei, F., Javidi, M., Mahmoudi, Y. New analytical methods for solving a class of conformable fractional differential equations by fractional Laplace transform. Computational Methods for Differential Equations, 2022; 10(2): 396-407. doi: 10.22034/cmde.2021.40834.1775