Global existence theory for fractional differential equations: New advances via continuation methods for contractive maps
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Saleh S. Almuthaybiri
and
Christopher C. Tisdell
Abstract
The aim of this article is to form new existence theory for global solutions to nonlinear fractional differential equations. Traditional approaches to existence, uniqueness and approximation of global solutions for initial value problems involving fractional differential equations have been unwieldy or intractable due to the limitations of previously used methods. This includes, for example, certain invariance conditions of the underlying local fixed point strategies. Herein we draw on an alternative tactics, applying the more modern ideas of continuation methods for contractive maps to fractional differential equations. In doing so, we shed new light on the situation, producing these new perspectives through a range of novel theorems that involve sufficient conditions under which global existence, uniqueness, approximation and location of solutions are ensured.
Funding statement: Saleh Almuthaybiri gratefully acknowledges his university (Qassim University) for having provided full financial support to make this research possible at The University of New South Wales.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Global existence theory for fractional differential equations: New advances via continuation methods for contractive maps
- On rough convergence of ρ-Cauchy sequence of triple sequences
- On the affirmative solution to Salem’s problem
- An elementary proof of Euler’s product expansion for the sine
Articles in the same Issue
- Frontmatter
- Global existence theory for fractional differential equations: New advances via continuation methods for contractive maps
- On rough convergence of ρ-Cauchy sequence of triple sequences
- On the affirmative solution to Salem’s problem
- An elementary proof of Euler’s product expansion for the sine
