{"references": ["1.\tAbdeljawad, T. (2015). On conformable fractional calculus. Journal of computational and Applied Mathematics, 279, 57-66. 2.\tAbu Hammad, I., & Khalil, R. (2014). Fractional Fourier series with applications. Am. J. Comput. Appl. Math, 4(6), 187-191. 3.\tAl-Horani, M., Hammad, M. A., & Khalil, R. (2016). Variation of parameters for local fractional nonhomogenous lineardifferential equations. J. Math. Computer Sci, 16, 147-153. 4.\tAl-Horani, M., Khalil, R., &Aldarawi, I. (2020).Fractional Cauchy Euler Differential Equation. Journal of Computational Analysis & Applications, 28(2). 5.\tAtangana, A., Baleanu, D., & Alsaedi, A. (2015). New properties of conformable derivative. Open Mathematics, 13(1). 6.\tAtangana, A., & Baleanu, D. (2016). New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. arXiv preprint arXiv:1602.03408. 7.\tBaleanu, D., G\u00fcven\u00e7, Z. B., & Machado, J. T. (Eds.). (2010). New trends in nanotechnology and fractional calculus applications (p. C397). New York: Springer. 8.\tCaputo, M., & Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progr. Fract. Differ. Appl, 1(2), 1-13. 9.\tContreras, A. O., Garc\u00eda, J. J. R., Jim\u00e9nez, L. M., & Cruz-Duarte, J. M. (2018). Analysis of projectile motion in view of conformable derivative. Open Physics, 16(1), 581-587. 10.\tDe Oliveira, E. C., & Tenreiro Machado, J. A. (2014). A review of definitions for fractional derivatives and integral. Mathematical Problems in Engineering, 2014. 11.\tFrunzo, L., Garra, R., Giusti, A., & Luongo, V. (2019). Modeling biological systems with an improved fractional Gompertz law. Communications in Nonlinear Science and Numerical Simulation, 74, 260-267. 12.\tGarcia, J. R., Calderon, M. G., Ortiz, J. M., Baleanu, D., & de Santiago, C. S. V. (2013). Motion of a particle in a resisting medium using fractional calculus approach. Proc. Romanian Acad. A, 14, 42-47. 13.\tG\u00f3mez, J. F., & Rosales, J. J., & Bernal, J. J. (2012). Mathematical modelling of the mass-spring-damper system - A fractional calculus approach . Acta Universitaria, 22(5),5-11. 14.\tHilfer, R. (Ed.). (2000). Applications of fractional calculus in physics. World scientific. 15.\tKatugampola, U. N. (2014). A new fractional derivative with classical properties. arXiv preprint arXiv:1410.6535. 16.\tKhalil, R., Al Horani, M., Yousef, A., &Sababheh, M. (2014).A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65-70. 17.\tKilbas, A. A., Marichev, O. I., & Samko, S. G. (1993). Fractional integrals and derivatives (theory and applications). 18.\tMartinez, L., Rosales, J. J., Carre\u00f1o, C. A., & Lozano, J. M. (2018). Electrical circuits described by fractional conformable derivative. International Journal of Circuit Theory and Applications, 46(5), 1091-1100. 19.\tMiller, K. S., & Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. Wiley. 20.\tOldham, K., & Spanier, J. (1974). The fractional calculus theory and applications of differentiation and integration to arbitrary order. Elsevier. 21.\tPodlubny, I. (1998). Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier. 22.\tPodlubny, I. (2001). Geometric and physical interpretation of fractional integration and fractional differentiation. arXiv preprint math/0110241. 23.\tRaisinghania, M. D. (2013). Ordinary and partial differential equations. S. Chand Publishing. 24.\tRosales, J., Gu\u00eda, M., G\u00f3mez, F., Aguilar, F., & Mart\u00ednez, J. (2014). Two dimensional fractional projectile motion in a resisting medium. Open Physics, 12(7), 517-520. 25.\tUchaikin, V. V. (2013). Fractional derivatives for physicists and engineers (Vol. 2). Berlin: Springer."]}

In this article, we introduce the concept of conformable linear fractional differential equations. General solutions for these equations are established. An attempt has been made to obtain particular integral for some special cases. This is achieved by obtaining a relationship between fractional integration and the usual integration. Finally, some real-world problems like the mass-spring-damper system and Gompertz Law of population growth are used to demonstrate the effectiveness of the theoretical findings.