Existence of the mild solution for fractional semilinear initial value problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 9, 2008, Pages 3153-3159

  Jaradat, Omar K ^a   Al Omari, Ahmad ^a   Momani, Shaher ^a  

^a MUTAH UNIVERSITY   (Jordan)

Author keywords

Existence and uniqueness; Fractional differential equation; Mild solution; Semilinear

Indexed keywords

INITIAL VALUE PROBLEMS; OPTIMAL CONTROL SYSTEMS; PARALLEL PROCESSING SYSTEMS;

EXISTENCE AND UNIQUENESS; FRACTIONAL DIFFERENTIAL EQUATION; MILD SOLUTION; MILD SOLUTIONS; SEMILINEAR;

DIFFERENTIAL EQUATIONS;

EID: 50349092768     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.09.008     Document Type: Article

References (9)

1. Barrett J. Differential equations of non-integer order. Canad. J. Math. 6 (1954) 529-541
2. Delbosco D., and Rodino L. Existence and uniqueness for a nonlinear fractional differential equation. J. Math. Anal. Appl. 204 (1996) 609-625
3. Hadid S.B., and Al-shamani J. Liapunov stability of D.E. of non-integer order. Arab. J. Maths 5 1-2 (1986) 5-17
4. He J.H. Some applications of nonlinear fractional differential equations and their approximations. Bull. Sci. Technol. 15 2 (1999) 86-90
5. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167 (1998) 57-68
6. Mainardi F. Fractional calculus 'Some basic problems in continuum and statistical mechanics'. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional calculus in Continuum Mechanics (1997), Springer-Verlag, New York 291-348
7. Miller K.S., and Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), John Wiley and Sons, Inc., New York
8. Podlubny I. Fractional Differential Equations (1999), Academic Press, New York
9. Caputo M. Linear models of dissipation whose q is almost frequency independent. Part II, J. Ray, Astr. Soc. 13 (1967) 529-539