Solving a class of random non-autonomous linear fractional differential equations by means of a generalized mean square convergent power series

We develop a new application of the Mittag-Leffler Function method that will extend the application of the method to linear differential equations with fractional order. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving linear differential equations of fractional order.

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Elzaki Transformation for Linear Fractional Differential Equations

Journal of Computational and Theoretical Nanoscience ◽

10.1166/jctn.2015.4221 ◽

2015 ◽

Vol 12 (9) ◽

pp. 2303-2305

Author(s):

Elsayed A. E. Mohamed

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Fractional Differential ◽

Linear Fractional Differential Equations

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Systems of Nonlinear Fractional Differential Equations

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2015-0008 ◽

2015 ◽

Vol 18 (1) ◽

Cited By ~ 3

Author(s):

Tadeusz Jankowski

Keyword(s):

Differential Equations ◽

Iterative Method ◽

Unique Solution ◽

Fractional Differential Equations ◽

Fractional Derivatives ◽

Nonlinear Fractional Differential Equations ◽

Fractional Differential ◽

The Right ◽

Linear Fractional Differential Equations

AbstractUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives $D^{q}_{T}x$ and $D^{q}_{T}y$. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.

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A Numerical Method for a Class of Linear Fractional Differential Equations

Mathematical Modelling and Scientific Computation - Communications in Computer and Information Science ◽

10.1007/978-3-642-28926-2_39 ◽

2012 ◽

pp. 360-366

Author(s):

V. Balakumar ◽

K. Murugesan

Keyword(s):

Differential Equations ◽

Numerical Method ◽

Fractional Differential Equations ◽

Fractional Differential ◽

Linear Fractional Differential Equations

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Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

International Journal of Differential Equations ◽

10.1155/2018/8686502 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 9

Author(s):

Mohammad Alaroud ◽

Mohammed Al-Smadi ◽

Rokiah Rozita Ahmad ◽

Ummul Khair Salma Din

Keyword(s):

Power Series ◽

Differential Equations ◽

Fractional Differential Equations ◽

Optimization Technique ◽

Fractional Power ◽

Taylor Formula ◽

Residual Power Series ◽

Fractional Differential ◽

Residual Power ◽

Fuzzy Fractional Differential Equations

This paper aims to present a novel optimization technique, the residual power series (RPS), for handling certain classes of fuzzy fractional differential equations of order 1<γ≤2 under strongly generalized differentiability. The proposed technique relies on generalized Taylor formula under Caputo sense aiming at extracting a supportive analytical solution in convergent series form. The RPS algorithm is significant and straightforward tool for creating a fractional power series solution without linearization, limitation on the problem’s nature, sort of classification, or perturbation. Some illustrative examples are provided to demonstrate the feasibility of the RPS scheme. The results obtained show that the scheme is simple and reliable and there is good agreement with exact solution.

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