Abstract
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.Â
Highlights
Basic definitionsFractional differential equations are studied in various fields of physics and engineering, in signal processing, control engineering, electromagnetism, biosciences, fluid mechanics, electrochemistry, diffusion processes, dynamic of viscoelastic material, continuum and statistical mechanics and propagation of spherical flames
Many effective methods have been proposed for the approximate solution fractional differential equations, such as Adomian decomposition method [3,4], homotopy perturbation method [5,6,7,8], homotopy analysis method [9,10], variational iteration method [11], generalized differential transform method [12] and other methods [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]
The general solution of this first order fractional differential equation based on conformable fractional derivative is
Summary
Fractional differential equations are studied in various fields of physics and engineering, in signal processing, control engineering, electromagnetism, biosciences, fluid mechanics, electrochemistry, diffusion processes, dynamic of viscoelastic material, continuum and statistical mechanics and propagation of spherical flames. There are many fractional differential equations which can’t be solved analytically Due to this fact, finding an approximate solution of fractional differential equations is clearly an important task. Many effective methods have been proposed for the approximate solution fractional differential equations, such as Adomian decomposition method [3,4], homotopy perturbation method [5,6,7,8], homotopy analysis method [9,10], variational iteration method [11], generalized differential transform method [12] and other methods [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. The purpose of this section is to recall some preliminaries of the proposed method
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