Vosoughi, H., Shivanian, E., Anbarloei, M. (2013). Multiple solutions of the nonlinear reaction-diusion model with fractional reaction. Theory of Approximation and Applications, 9(2), 159-170.

H. Vosoughi; E. Shivanian; M. Anbarloei. "Multiple solutions of the nonlinear reaction-diusion model with fractional reaction". Theory of Approximation and Applications, 9, 2, 2013, 159-170.

Vosoughi, H., Shivanian, E., Anbarloei, M. (2013). 'Multiple solutions of the nonlinear reaction-diusion model with fractional reaction', Theory of Approximation and Applications, 9(2), pp. 159-170.

Vosoughi, H., Shivanian, E., Anbarloei, M. Multiple solutions of the nonlinear reaction-diusion model with fractional reaction. Theory of Approximation and Applications, 2013; 9(2): 159-170.

Multiple solutions of the nonlinear reaction-diusion model with fractional reaction

^{1}Department of Mathematics, Faculty of Science, Islamshahr Branch, Islamic Azad University, Islamshahr, Tehran, Iran

^{2}Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran

Abstract

The purpose of this letter is to revisit the nonlinear reaction-diusion model in porous catalysts when reaction term is fractional function of the concen- tration distribution of the reactant. This model, which originates also in uid and solute transport in soft tissues and microvessels, has been recently given analytical solution in terms of Taylors series for dierent family of reaction terms. We apply the method so-called predictor homotopy analysis method (PHAM) which has been recently proposed to predict multiplicity of solutions of nonlinear BVPs. Consequently, it is indicated that the problem for some values of the parameter admits multiple solutions. Also, error analysis of these solutions are given graphically.

Article Title [Persian]

Multiple solutions of the nonlinear
reaction-diusion model with fractional
reaction

Authors [Persian]

H. Vosoughi^{1}; E. Shivanian^{2}; M. Anbarloei^{1}

^{1}Department of Mathematics, Faculty of Science, Islamshahr Branch,
Islamic Azad University, Islamshahr, Tehran, Iran

^{2}Department of Mathematics, Imam Khomeini International University,
Qazvin, 34149-16818, Iran

Abstract [Persian]

The purpose of this letter is to revisit the nonlinear reaction-diusion model in porous catalysts when reaction term is fractional function of the concen- tration distribution of the reactant. This model, which originates also in uid and solute transport in soft tissues and microvessels, has been recently given analytical solution in terms of Taylors series for dierent family of reaction terms. We apply the method so-called predictor homotopy analysis method (PHAM) which has been recently proposed to predict multiplicity of solutions of nonlinear BVPs. Consequently, it is indicated that the problem for some values of the parameter admits multiple solutions. Also, error analysis of these solutions are given graphically.

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