A novel approach to approximate fractional derivative with uncertain conditions. (November 2017)

• Record Type: Journal Article
• Authors: Ahmadian, A.; Salahshour, S.; Ali-Akbari, M.; Ismail, F.; Baleanu, D.
• Is Part Of: Chaos, solitons and fractals. Volume 104(2017)
• Page Start: 68
• Page End: 76
• Publication Date: 2017-11
• Subjects: Fractional differential equations -- Caputo-type derivative -- Laplace transforms -- Basset problem -- Uncertainty; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.07.026
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: To approximate the fractional derivative base on generalized differentiability in a simple way. To employ a linearization technique to reduce the complexity of the original problem. To present an efficient technique base on Laplace transforms to achieve the fuzzy approximate solution. To apply the algorithm for real-world applications in nature. To propose a Derivative theorem to simplify the problems to get the numerical solution. Abstract: This paper focuses on providing a new scheme to find the fuzzy approximate solution of fractional differential equations (FDEs) under uncertainty. The Caputo-type derivative base on the generalized Hukuhara differentiability is approximated by a linearization formula to reduce the corresponding uncertain FDE to an ODE under fuzzy concept. This new approach may positively affect on the computational cost and easily apply for the other types of uncertain fractional-order differential equation. The performed numerical simulations verify the proficiency of the presented scheme.