Operational matrix for Atangana–Baleanu derivative based on Genocchi polynomials for solving FDEs
By S. Sadeghi, Hossein Jafari, Somayeh Nemati. 2020
52 citations recorded by the source corpus.
Abstract Recently, Atangana and Baleanu have defined a new fractional derivative which has a nonlocal and non-singular kernel. It is called the Atangana–Baleanu derivative. In this paper we present a numerical technique to obtain solution of fractional differential equations containing Atangana–Baleanu derivative. For this purpose, we use the operational matrices based on Genocchi polynomials together with the collocation points which help us to reduce the problem to a system of algebraic equations. An error bound for the error of the operational matrix of the fractional derivative is introduced. Finally, some examples are given to illustrate the applicability and efficiency of the proposed method.
Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/94459d43a98af3ee12747f5e070addb13abbf5f6
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In Modeling and Simulation
- Khosro Sayevand
- Dumitru Băleanu
- Roghayeh Moallem Ganji
- Hossein Jafari
- Mehdi Dehghan
- Thabet Abdeljawad
- Arran Fernandez
- Abdon Atangana
In Numerical Analysis
- Khosro Sayevand
- Dumitru Băleanu
- Roghayeh Moallem Ganji
- Hossein Jafari
- Arran Fernandez
- Thabet Abdeljawad
- Mehdi Dehghan
- Abdon Atangana
In Statistical and Nonlinear Physics
- Dumitru Băleanu
- Khosro Sayevand
- Hossein Jafari
- Guo-cheng Wu
- Thabet Abdeljawad
- Mehdi Dehghan
- Delfim F. M. Torres
- Om Prakash Agrawal
Citations in the corpus
- A numerical approach for solving fractional optimal control problems with mittag-leffler kernel (2021, methodology): “…as a useful tool in solving many classes of equations numerically, for example, differential equations (Ganji et al., 2020a; Jafari et al., 2019; Sadeghi et al., 2020), partial differential equations (Tajadodi, 2020; Tuan et al., 2020b), integro-differential equations (Ganji et al., 2020b;…”