One of the aims of this article is to investigate the solvability and unsolvability conditions for fractional cohomological equation ψ αf = g, on T n. We prove that if f is not analytic, then fractional integro-differential equation I 1−α t Dα x u(x, t) + iI1−α x Dα t u(x, t) = f(t) has no solution in C1 (B) with 0 < α ≤ 1. We also obtain solutions for the space-time fractional heat equations on S 1 and T n. At the end of this article, there are examples of fractional partial differential equations and a fractional integral equation together with their solutions.
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Dehghan Nezhad, A., Moghaddam, M. (2021). Toward a new understanding of cohomological method for fractional partial differential equations. Computational Methods for Differential Equations, 9(4), 959-976. doi: 10.22034/cmde.2020.39020.1710
MLA
Akbar Dehghan Nezhad; Mina Moghaddam. "Toward a new understanding of cohomological method for fractional partial differential equations". Computational Methods for Differential Equations, 9, 4, 2021, 959-976. doi: 10.22034/cmde.2020.39020.1710
HARVARD
Dehghan Nezhad, A., Moghaddam, M. (2021). 'Toward a new understanding of cohomological method for fractional partial differential equations', Computational Methods for Differential Equations, 9(4), pp. 959-976. doi: 10.22034/cmde.2020.39020.1710
VANCOUVER
Dehghan Nezhad, A., Moghaddam, M. Toward a new understanding of cohomological method for fractional partial differential equations. Computational Methods for Differential Equations, 2021; 9(4): 959-976. doi: 10.22034/cmde.2020.39020.1710