Journal
ADVANCES IN DIFFERENCE EQUATIONS
Volume -, Issue -, Pages -Publisher
SPRINGEROPEN
DOI: 10.1186/s13662-019-2082-8
Keywords
Bagley-Torvik equation; Novel max-metric; Existence and uniqueness; Analytical solution; Caputo derivative
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Funding
- National Natural Science Foundation of China [11371027, 11471015, 11771001, 11601003]
- China Scholarship Council
- Natural Science Foundation of Colleges and Universities in Anhui Province [KJ2018A0470]
- Natural Science Foundation of Anhui Province [1708085MA15]
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In this paper, we investigate the generalized Bagley-Torvik equation with the fractional order (0,2). With a novel max-metric containing a Caputo derivative, the existence and uniqueness of the solution to the initial value problem are derived. We obtain the analytical solutions in terms of the Prabhakar function and the Wiman function, and they expand the well-known results about the general Bagley-Torvik equation. Two examples are presented to illustrate the validity of our main results.
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