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NUMERICAL SOLUTIONS OF SOME KINDS OF FRACTIONAL DIFFERENTIAL EQUATIONS

‎L‎. ‎N‎. ‎M‎. Tawfiq, Iman Isho Gorial

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Abstract

In this paper we present and discuss an algorithm for the numerical solution of some kinds of fractional differential equations, i.e. of order n+v, n ≤ 3, 2 nd order 2v and nv, n ≥ 3. The algorithm for the numerical solution of these equations is based on a Newton approach. The stability and convergence of the fractional order numerical method are described. Finally, some numerical examples are provided to show that the numerical method for solving the fractional differential equation is an effective solution method.

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What this paper is about

In this paper we present and discuss an algorithm for the numerical solution of some kinds of fractional differential equations, i.e. of order n+v, n ≤ 3, 2 nd order 2v and nv, n ≥ 3. The algorithm for the numerical solution of these equations is based on a Newton approach. The stability and convergence of the fractional order numerical method are described. Finally, some numerical examples are provided to show that the numerical method for solving the fractional differential equation is an effective solution method.

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Available abstract

In this paper we present and discuss an algorithm for the numerical solution of some kinds of fractional differential equations, i.e. of order n+v, n ≤ 3, 2 nd order 2v and nv, n ≥ 3. The algorithm for the numerical solution of these equations is based on a Newton approach. The stability and convergence of the fractional order numerical method are described. Finally, some numerical examples are provided to show that the numerical method for solving the fractional differential equation is an effective solution method.

Key concepts: Mathematics, Numerical stability, Numerical analysis, Order of accuracy, Convergence (economics), Stability (learning theory), Differential equation, Mathematical analysis

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