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Approximate Solution of Fractional Order Lane–Emden Type Differential Equation by Orthonormal Bernoulli’s Polynomials

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Abstract

An approximate method based on orthonormal Bernoulli’s polynomials together with their operational matrices is applied for solving fractional order differential equations of Lane–Emden type. The preliminaries of fractional calculus are first presented. Operational matrices of fractional derivative and integer order derivative are constructed in this article. Convergence analysis of orthonormal Bernoulli’s polynomials is proposed here. By using this method, the fractional Lane–Emden differential equation converted into a system of algebraic equations by applying some suitable collocation points and this system can be simplified by an appropriate numerical method. Examples are illustrated to show the validity and applicability of the present method.

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This article is part of the topical collection “Recent Advances in Mathematics and its Applications” edited by Santanu Saha Ray.

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Sahu, P.K., Mallick, B. Approximate Solution of Fractional Order Lane–Emden Type Differential Equation by Orthonormal Bernoulli’s Polynomials. Int. J. Appl. Comput. Math 5, 89 (2019). https://doi.org/10.1007/s40819-019-0677-0

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