General solution of second order fractional differential equations


  • Mousa Ilie Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
  • Jafar Biazar Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O.Box.41335-1914, Guilan, Rasht, Iran
  • Zainab Ayati Department of Engineering sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran





Linear fractional differential equations, Conformable fractional derivative, Constant coefficients approach, Euler’s equation, Variation of parameters, Lagrange method, Undetermined coefficients,


Fractional differential equations are often seeming perplexing to solve. Therefore, finding comprehensive methods for solving them sounds of high importance. In this paper, a general method for solving second order fractional differential equations has been presented based on conformable fractional derivative. This method realizes on determining a general solution of homogeneous and a particular solution of a second order linear fractional differential equations. Furthermore, a general solution has been developed for fractional Euler’s equation. For more explanation of each part, some examples have been solved. 


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