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- W2803329712 abstract "In this work, we propose a novel analytical solution approach for solving a general homogeneous time-invariant fractional initial value problem in the normal form $$begin{aligned}& D_{t}^{alpha } bigl[u(overline{x},t) bigr] = F bigl(u( overline{x},t) bigr),quad 0leq t < R, & u(overline{x},0) = f(overline{x}), end{aligned}$$ where $D_{t}^{alpha }$ is the Caputo fractional operator with $0<alpha leq 1$ . The solution is given analytically in the form of a convergent multi-fractional power series without using any particular treatments for the nonlinear terms. The new approach is taken to search patterns for compacton solutions of several nonlinear time-fractional dispersive equations, namely $K_{alpha }(2,2)$ , $ZK_{alpha }(2,2)$ , $DD_{alpha }(1,2,2)$ , and $K_{alpha }(2,2,1)$ . Remarkably, the graphical analysis showed that the n-term approximate memory solutions, labeled by the memory parameter $0<alpha leq 1$ , are continuously homotopic as they reflect, in some sense, some memory and heredity properties." @default.
- W2803329712 created "2018-06-01" @default.
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- W2803329712 date "2018-04-20" @default.
- W2803329712 modified "2023-09-27" @default.
- W2803329712 title "Analytic solution of homogeneous time-invariant fractional IVP" @default.
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- W2803329712 doi "https://doi.org/10.1186/s13662-018-1601-3" @default.
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