zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives. (English) Zbl 1172.26307
By employing the method of monotone iteration, a result on the existence and uniqueness of a solution of the initial value problem for fractional differential equation $$D\sp{\alpha}u(t)= f(t,u), \quad t\in (0,T], \qquad t\sp{1-\alpha}u(t)\mid\sb{t=0} = u\sb 0, $$ where $0<T<+\infty$ and $D\sp{\alpha}$ is the Riemann-Liouville fractional derivative of order $0<\alpha<1$ is established and discussed.

26A33Fractional derivatives and integrals (real functions)
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34A40Differential inequalities (ODE)
34A99General theory of ODE
Full Text: DOI
[1] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations. (2006) · Zbl 1092.45003
[2] Pitcher, E.; Sewell, W. E.: Existence theorems for solutions of differential equations of non-integral order. Bull. amer. Math. soc.. 44, No. 2, 100-107 (1938) · Zbl 0018.30701
[3] Al-Bassam, M. A.: Some existence theorems on differential equations of generalized order. J. reine angew. Math. 218, No. 1, 70-78 (1965) · Zbl 0156.30804
[4] Delbosco, D.; Rodino, L.: Existence and uniqueness for a nonlinear fractional differential equation. J. math. Anal. appl. 204, No. 2, 609-625 (1996) · Zbl 0881.34005
[5] Kilbas, A. A.; Marzan, S. A.: Nonlinear differential equations in weighted spaces of continuous functions. Dokl. nats. Akad. nauk belarusi 47, No. 1, 29-35 (2003) · Zbl 1204.26009
[6] Rivero, M.; Rodriguez-Germa, L.; Trujillo, J. J.: Linear fractional differential equations with variable coefficients. Appl. math. Lett. 21, 892-897 (2008) · Zbl 1152.34305
[7] Ibrahim, Rabha W.; Darus, Maslina: Subordination and superordination for univalent solutions for fractional differential equations. J. math. Anal. appl. 345, 871-879 (2008) · Zbl 1147.30009
[8] Zhang, Shuqin: The existence of a positive solution for a nonlinear fractional differential equation. J. math. Anal. appl. 252, 804-812 (2000) · Zbl 0972.34004
[9] Zhang, Shuqin: Positive solution for some class of nonlinear fractional differential equation. J. math. Anal. appl. 278, No. 1, 136-148 (2003) · Zbl 1026.34008
[10] J.V. Devi, V. Lakshmikantham, Nonsmooth analysis and fractional differential equations, Nonlinear Anal. IMA, (in press) · Zbl 1237.49022
[11] Y.-K. Chang, J.J. Nieto, Some new existence results for fractional differential inclusions with boundary conditions, Math. Comput. Modelling (in press) · Zbl 1165.34313
[12] N. Kosmatov, Integral equations and initial value problems for nonlinear differential equations of fractional order, Nonlinear Anal. TMA, in press, (doi:10.1016/j.na.2008.03.037) · Zbl 1169.34302
[13] Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S.: Monotone iterative techniques for nonlinear differential equations. (1985) · Zbl 0658.35003
[14] Pao, C. V.: Nonlinear parabolic and elliptic equations. (1992) · Zbl 0777.35001
[15] Ahmad, B.; Sivasundaram, S.: Existence results and monotone iterative technique for impulsive hybrid functional differential systems with anticipation and retardation. Appl. math. Comput. 197, 515-524 (2008) · Zbl 1142.34049
[16] Bhaskar, T. G.; Lakshmikantham, V.; Devi, J. V.: Monotone iterative technique for functional differential equations with retardation and anticipation. Nonlinear anal. TMA 66, 2237-2242 (2007) · Zbl 1121.34065
[17] Nieto, J. J.; Rodriguez-Lopez, R.: Monotone method for first-order functional differential equations. Comput. math. Appl. 52, 471-484 (2006) · Zbl 1140.34406
[18] Jiang, D.; Nieto, J. J.; Zuo, W.: On monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations. J. math. Anal. appl. 289, 691-699 (2004) · Zbl 1134.34322
[19] Nieto, J. J.; Rodriguez-Lopez, R.: Boundary value problems for a class of impulsive functional equations. Comput. math. Appl. 55, 2715-2731 (2008) · Zbl 1142.34362
[20] Lakshmikanthan, V.; Vatsala, A. S.: Basic theory of fractional differential equations. Nonlinear anal. TMA 69, No. 8, 2677-2682 (2008) · Zbl 1161.34001