Well-posedness of general Caputo-type fractional differential equations

By C. Sin. Fractional Calculus and Applied Analysis, 2018

50 citations recorded by the source corpus.

Abstract In the present paper, initial value problems of fractional differential equations are considered. The fractional derivatives are defined as the general Caputo-type fractional derivatives proposed by Anatoly Kochubei. By using the Schauder fixed point theorem, the local existence, the global existence and the uniqueness of solutions are obtained under appropriate conditions. In addition, it is proved that the solution depends on the parameters of the equation in a continuous way.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3b4bd3d6f69e6926cc1f1e7253518f80b08ecc36

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense (2022, background): “, [7, 8, 9, 11, 12, 13, 14, 21]), to the best of author’s knowledge, only one publication dealing with the fractional differential equations with the GFDs in the Riemann-Liouville sense has been published until now.”
On History of Mathematical Economics: Application of Fractional Calculus (2019, methodology): “The existence of a solution in the growth case has been also proved in 2018 by Chung-Sik Sin [243] for nonlinear equation with a generalized derivative like the Kochubei fractional derivative.”
The General Fractional Derivative and Related Fractional Differential Equations (2020, methodology): “The Cauchy Problem for a Nonlinear Fractional ODE Following [14], in this subsection, we address a nonlinear fractional differential equation with the GFD of the Caputo type (DCk u)(t) = f (t, u(t)), t > 0 (43) subject to the initial condition u(0) = u0 ∈ R. (44) In what follows, we again assume tha”
General Fractional Integrals and Derivatives with the Sonine Kernels (2021, methodology): “The ordinary fractional differential equations with the Caputo type GFDs are addressed in [1,5–7] and the time-fractional diffusion equations with these derivatives are considered in [1, 3, 5, 8–10].”
Operational Calculus for the General Fractional Derivative and Its Applications (2021, unknown): “In the meantime, some advanced results for the ordinary and partial time-fractional differential equations with the GFDs have been derived (see [15, 17, 18, 34] for the ODEs and [15–17,27,28,33] for the PDEs with the GFDs).”