Existence of solutions for the semilinear abstract Cauchy problem of fractional order
-
Hernán R. Henríquez
,
Verónica Poblete
Abstract
In this paper we establish the existence of solutions for the nonlinear abstract Cauchy problem of order α ∈ (1, 2), where the fractional derivative is considered in the sense of Caputo. The autonomous and nonautonomous cases are studied. We assume the existence of an α-resolvent family for the homogeneous linear problem. By using this α-resolvent family and appropriate conditions on the forcing function, we study the existence of classical solutions of the nonhomogeneus semilinear problem. The non-autonomous problem is discussed as a perturbation of the autonomous case. We establish a variation of the constants formula for the nonautonomous and nonhomogeneous equation.
Acknowledgements
The authors are very grateful to the editor and the anonymous reviewers for their careful reading of the manuscript, comments and suggestions, which allowed to significantly improve the original version of the text.
H. R. Henríquez was partially supported by Vicerrectoría de Investigación, Desarrollo e Innovación de la Universidad de Santiago under Grant DICYT-USACH 041733HM; V. Poblete was partially supported by project Fondecyt 1191137, and J. C. Pozo was partially supported by project Fondecyt 1181084.
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© 2021 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books
- Survey Paper
- Towards a unified theory of fractional and nonlocal vector calculus
- Research Paper
- An adaptive memory method for accurate and efficient computation of the Caputo fractional derivative
- Analysis of solutions of some multi-term fractional Bessel equations
- Existence of solutions for the semilinear abstract Cauchy problem of fractional order
- Summability of formal solutions for a family of generalized moment integro-differential equations
- Analysis and fast approximation of a steady-state spatially-dependent distributed-order space-fractional diffusion equation
- Green’s function for the fractional KdV equation on the periodic domain via Mittag–Leffler function
- First order plus fractional diffusive delay modeling: Interconnected discrete systems
- On a solution of a fractional hyper-Bessel differential equation by means of a multi-index special function
- On the decomposition of solutions: From fractional diffusion to fractional Laplacian
- Output error MISO system identification using fractional models
- Short Paper
- Identification of system with distributed-order derivatives
- Short note
- On the Green function of the killed fractional Laplacian on the periodic domain
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books
- Survey Paper
- Towards a unified theory of fractional and nonlocal vector calculus
- Research Paper
- An adaptive memory method for accurate and efficient computation of the Caputo fractional derivative
- Analysis of solutions of some multi-term fractional Bessel equations
- Existence of solutions for the semilinear abstract Cauchy problem of fractional order
- Summability of formal solutions for a family of generalized moment integro-differential equations
- Analysis and fast approximation of a steady-state spatially-dependent distributed-order space-fractional diffusion equation
- Green’s function for the fractional KdV equation on the periodic domain via Mittag–Leffler function
- First order plus fractional diffusive delay modeling: Interconnected discrete systems
- On a solution of a fractional hyper-Bessel differential equation by means of a multi-index special function
- On the decomposition of solutions: From fractional diffusion to fractional Laplacian
- Output error MISO system identification using fractional models
- Short Paper
- Identification of system with distributed-order derivatives
- Short note
- On the Green function of the killed fractional Laplacian on the periodic domain
