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Solving a well-posed fractional initial value problem by a complex approach
- Publication Year :
- 2021
- Publisher :
- Springer Nature, 2021.
-
Abstract
- Uçar, Sümeyra (Balikesir Author)<br />Nonlinear fractional differential equations have been intensely studied using fixed point theorems on various different function spaces. Here we combine fixed point theory with complex analysis, considering spaces of analytic functions and the behaviour of complex powers. It is necessary to study carefully the initial value properties of Riemann–Liouville fractional derivatives in order to set up an appropriate initial value problem, since some such problems considered in the literature are not well-posed due to their initial conditions. The problem that emerges turns out to be dimensionally consistent in an unexpected way, and therefore suitable for applications too. © 2021, The Author(s).
- Subjects :
- Function space
Fixed Point Theorems
Fractional Differential Equations
010102 general mathematics
Fixed-point theorem
01 natural sciences
Well-Posedness
Fractional calculus
010101 applied mathematics
Set (abstract data type)
Differential geometry
Initial Value Problems
Nonlinear Differential Equations
Applied mathematics
Initial value problem
0101 mathematics
Existence-Uniqueness Problems
Topology (chemistry)
Mathematics
Analytic function
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....7cf9a38e6880c3005f2cbd96adebdcad