General solution of second order fractional differential equations

• Authors

• 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
2018-05-20
• Linear fractional differential equations, Conformable fractional derivative, Constant coefficients approach, Eulerâ€™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 Eulerâ€™s equation. For more explanation of each part, some examples have been solved.Â

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