Solving a well-posed fractional initial value problem by a complex approach
DOI10.1186/s13663-021-00696-2OpenAlexW3169201557MaRDI QIDQ2138442
Arran Fernandez, Necati Özdemir, Sümeyra Uçar
Publication date: 12 May 2022
Published in: Fixed Point Theory and Algorithms for Sciences and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1186/s13663-021-00696-2
nonlinear differential equationswell-posednessinitial value problemsfixed point theoremsfractional differential equationsexistence-uniqueness problems
Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Entire and meromorphic solutions to ordinary differential equations in the complex domain (34M05) Fractional ordinary differential equations (34A08)
Cites Work
- Unnamed Item
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- Approximate controllability of fractional neutral evolution equations in Banach spaces
- How to impose physically coherent initial conditions to a fractional system?
- The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
- An operational method for solving fractional differential equations with the Caputo derivatives
- Complex variable approach to the analysis of a fractional differential equation in the real line
- The Nehari manifold for a boundary value problem involving Riemann-Liouville fractional derivative
- Advances in applied mathematics and approximation theory. Contributions from AMAT 2012 -- International conference on applied mathematics and approximation theory, Ankara, Turkey, May 17--20, 2012
- Existence of positive periodic solutions of some nonlinear fractional differential equations
- Solving PDEs of fractional order using the unified transform method
- Dynamical analysis of fractional order model for computer virus propagation with kill signals
- Existence and uniqueness of positive solutions for nonlinear fractional mixed problems
- Comments on: ``The failure of certain fractional calculus operators in two physical models
- A new collection of real world applications of fractional calculus in science and engineering
- Hadamard-type fractional calculus in Banach spaces
- Solvability of a non-local problem with integral transmitting condition for mixed type equation with Caputo fractional derivative
- Explicit analytical solutions of incommensurate fractional differential equation systems
- Two–dimensional linear partial differential equations in a convex polygon
- The Dbar formalism for certain linear non-homogeneous elliptic PDEs in two dimensions
- Analytical schemes for a new class of fractional differential equations
- A Unified Approach to Boundary Value Problems
- A unified transform method for solving linear and certain nonlinear PDEs
- Boundary‐value problems for the third‐order loaded equation with noncharacteristic type‐change boundaries
- A generalisation of the Malgrange–Ehrenpreis theorem to find fundamental solutions to fractional PDEs
- Basic Theory
- Complexification and integrability in multidimensions
- On solutions of variable-order fractional differential equations
- New complex exact travelling wave solutions for the generalized-Zakharov equation with complex structures
- Fractionalisation of complex d-bar derivatives
- Fractional Calculus
