Non-probabilistic Solutions of Uncertain Fractional Order Diffusion Equations

• Published in: Fundamenta informaticae Vol. 133; no. 1; pp. 19 - 34
• Main Authors: Tapaswini, Smita, Chakraverty, S.
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.01.2014
• Subjects: Crisps; Diffusion; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy systems; Mathematical analysis; Mathematical models; homotopy perturbation method; triangular fuzzy number; fuzzy fractional diffusion equation; double parametric form of fuzzy number
• ISSN: 0169-2968; 1875-8681
• DOI: 10.3233/FI-2014-1060

This paper investigates the numerical solution of uncertain fractional order diffusion equation subject to various external forces. Homotopy Perturbation Method (HPM) is used for the analysis. Uncertainties present in the system are modelled through triangular convex normalised fuzzy sets. A new computational technique has been proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy fractional diffusion equation is converted first to an interval fuzzy fractional differential equation. Next this equation is transformed to crisp form by applying double parametric form of fuzzy numbers. Finally the same is solved by HPM symbolically to obtain the uncertain bounds of the solution. Obtained results are depicted in term of plots. Results obtained by the proposed method are compared with existing results in special cases.