Fractional Cauchy problems for infinite interval case

Mohammed Al Horani; Mauro Fabrizio; Angelo Favini; Hiroki Tanabe

doi:10.3934/dcdss.2020240

Article Contents

2020, Volume 13, Issue 12: 3285-3304. Doi: 10.3934/dcdss.2020240

This issue Previous Article Preface to this special issue Next Article Fractional Ostrowski-Sugeno Fuzzy univariate inequalities

Fractional Cauchy problems for infinite interval case

1.
Department of Mathematics, The University of Jordan, Amman, Jordan
2.
Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5 - 40126 Bologna, Italy
3.
Takarazuka, Hirai Sanso 12-13,665-0817, Japan

^* Corresponding author: Mohammed Al Horani
^* Corresponding author: Mohammed Al Horani

Received: November 30, 2018

Revised: September 30, 2019

Early access: January 2020

Published: August 2020

Abstract Full Text(HTML) Related Papers Cited by

Abstract

We are devoted with fractional abstract Cauchy problems. Required conditions on spaces and operators are given guaranteeing existence and uniqueness of solutions. An inverse problem is also studied. Applications from partial differential equations are given to illustrate the abstract fractional degenerate differential problems.

Keywords:

Mathematics Subject Classification: Primary: 26A33; Secondary: 34G10.

Citation:

Full Text(HTML)

Related Papers

Cited by

References

[1]	M. Al Horani, A. Favini and H. Tanabe, Direct and inverse fractional abstract Cauchy problems, Mathematics, 7 (2019), 1-9.
[2]	M. Al Horani, M. Fabrizio, A. Favini and H. Tanabe, Fractional Cauchy problems and applications, Discrete & Continuous Dynamical Systems-Series S, to appear.
[3]	M. Al Horani, M. Fabrizio, A. Favini and H. Tanabe, Direct and inverse problems for degenerate differential equations, Ann. Univ. Ferrara, 64 (2018), 227-241. doi: 10.1007/s11565-018-0303-9.
[4]	E. G. Bazhlekova,, Fractional Evolution Equations in Banach Spaces, Eindhoven University of Technology, 2001.
[5]	A. Favaron, A. Favini and H. Tanabe, Perturbation methods for inverse problems on degenerate differential equations, preprint.
[6]	A. Favini, A. Lorenzi, G. Marinoschi and H. Tanabe, Perturbation methods and identification problems for degenerate evolution systems, Advances in Mathematics, Ed. Acad. Române, Bucharest, (2013), 145-156.
[7]	A. Favini, A. Lorenzi and H. Tanabe, Degenerate integro-differential equations of parabolic type with Robin boundary conditions, Journal of Mathematical Analysis and Applications, 447 (2017), 579-665. doi: 10.1016/j.jmaa.2016.10.029.
[8]	A. Favini, A. Lorenzi and H. Tanabe, Direct and inverse degenerate parabolic differential equations with multi-valued operators, Electron. J. Diff. Equ., 2015 (2015), 1-22.
[9]	A. Favini, A. Lorenzi and H. Tanabe, Singular integro-differential equations of parabolic type, Advances in Differential Equations, 7 (2002), 769-798.
[10]	A. Favini and H. Tanabe, Degenerate differential equations of parabolic type and inverse problems, Proceeding, Seminar on Partial Differential Equations, Osaka University, Osaka (2015), 89-100.
[11]	A. Favini and A. Yagi, Multivalued linear operators and degenerate evolution equations, Annali Di Matematica Pura ed Applicata, 163 (1993), 353-384. doi: 10.1007/BF01759029.
[12]	A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc. New York, 1999.
[13]	V. Fedorov and N. D. Ivanova, Identification problem for degenerate evolution equations of fractional order, Fractional Calculus and Applied Analysis, 20 (2017), 706-721.
[14]	D. Guidetti, On maximal regularity for the Cauchy-Dirichlet mixed parabolic problem with fractional time derivative, Bruno Pini Mathematical Analysis Seminar, 9 (2018), 147-157.
[15]	T. Kato, Fractional powers of dissipative operators, J. Math. Soc. Japan, 13 (1961), 246-274. doi: 10.2969/jmsj/01330246.
[16]	J. L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems And Applications, Springer-Verlag, Berlin, 1972.
[17]	J. L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Publications Mathmatiques de l'IHES, 19 (1964), 5-68.
[18]	A. Lorenzi, An Introduction to Identification Problems Via Functional Analysis, VSP, Utrecht, The Netherland, 2001.
[19]	G. A. Sviridyuk and V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht, Boston, 2003.
[20]	H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amesterdam, 1978.