zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Some generalizations of comparison results for fractional differential equations. (English) Zbl 1232.34014
Summary: By using the technique of upper and lower solutions together with the theory of strict and nonstrict fractional differential inequalities involving Riemann-Liouville differential operator of order q, 0<q<1, some necessary comparison results for further generalizations of several dynamical concepts are obtained. Furthermore, these results are extended to the finite systems of fractional differential equations.
MSC:
34A08Fractional differential equations
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
45J05Integro-ordinary differential equations
References:
[1]Caputo, M.: Linear model of dissipation whose Q is almost frequency independent-II, Geophysical J. Royal astronomic society 13, 529-539 (1967)
[2]Samko, S. G.; Kilbas, A. A.; Maritchev, O. I.: Fractional integrals and derivatives: theory and applications, (1993) · Zbl 0818.26003
[3]Metzler, R.; Schick, W.; Kilian, H. G.; Nonnenmacher, T. F.: Relaxation in filled polymers: a fractional calculus approach, The journal of chemical physics 103, No. 16, 7180-7186 (1995)
[4], Applications of fractional calculus in physics (2000)
[5]Kiryakova, V.: Generalized fractional calculus and applications, Pitman res. Notes math. Ser. 301 (1994) · Zbl 0882.26003
[6]Glockle, W. G.; Nonnenmacher, T. F.: A fractional calculus approach to self-similar protein dynamics, Biophysical journal 68, No. 1, 46-53 (1995)
[7]Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation, Fractional calculus applied analysis 5, No. 4, 367-386 (2002) · Zbl 1042.26003
[8]Lakshmikantham, V.; Leela, S.; Devi, J. Vasundhara: Theory of fractional dynamic systems, (2009)
[9]Kilbas, A. A.; Srivatsava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[10]Podlubny, I.: Fractional differential equations, (1999)
[11]Agarwal, R. P.; Benchohra, M.; Hamani, S.: A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta applicandae mathematicae 109, No. 3, 973-1033 (2010) · Zbl 1198.26004 · doi:10.1007/s10440-008-9356-6
[12]Lakshmikantham, V.; Vatsala, A. S.: Theory of fractional differential inequalities and applications, Communications in applied analysis 11, 395-402 (2008) · Zbl 1159.34006
[13]Lakshmikantham, V.; Devi, J. Vasundhara: Theory of fractional differential equations in a Banach space, European journal of pure and applied mathematics 1, No. 1, 38-45 (2008) · Zbl 1146.34042 · doi:http://www.ejpam.com/ejpam/index.php/ejpam/article/view/84
[14]Lakshmikantham, V.; Vatsala, A. S.: Basic theory of fractional differential equations, Nonlinear analysis TMA 69, No. 8, 2677-2682 (2008) · Zbl 1161.34001 · doi:10.1016/j.na.2007.08.042
[15]Lakshmikantham, V.; Vatsala, A. S.: General uniqueness and monotone iterative technique for fractional differential equations, Applied mathematics letters 21, No. 8, 828-834 (2008) · Zbl 1161.34031 · doi:10.1016/j.aml.2007.09.006
[16]Lakshmikantham, V.; Leela, S.: A Krasnoselskii–Krein-type uniqueness result for fractional differential equations, Nonlinear analysis TMA 71, No. 7–8, 3421-3424 (2009) · Zbl 1177.34004 · doi:10.1016/j.na.2009.02.008
[17]Daftardar-Gejji, V.; Babakhani, A.: Analysis of a system of fractional differential equations, Journal of mathematical analysis and applications 293, No. 2, 511-522 (2004) · Zbl 1058.34002 · doi:10.1016/j.jmaa.2004.01.013
[18]Baleanu, D.; Trujillo, J. I.: A new method of finding the fractional Euler–Lagrange and Hamilton equations within Caputo fractional derivatives, Communications in nonlinear science and numerical simulation 15, No. 5, 1111-1115 (2010) · Zbl 1221.34008 · doi:10.1016/j.cnsns.2009.05.023
[19]Baleanu, D.; Mustafa, O. G.: On the global existence of solutions to a class of fractional differential equations, Computers mathematics with applications 59, No. 5, 1835-1841 (2010) · Zbl 1189.34006 · doi:10.1016/j.camwa.2009.08.028
[20]Benchohra, M.; Hamani, S.; Ntouyas, S. K.: Boundary value problems for differential with fractional order, Surveys in mathematics and its applications 3, 1-12 (2008) · Zbl 1157.26301 · doi:http://www.utgjiu.ro/math/sma/v03/a01.html
[21]Chang, Y. -K.; Nieto, J. J.: Some new existence results for fractional differential inclusions with boundary conditions, Mathematical and computer modelling 49, No. 3–4, 605-609 (2009) · Zbl 1165.34313 · doi:10.1016/j.mcm.2008.03.014
[22]Ouahab, A.: Some results for fractional boundary value problem of differential inclusions, Nonlinear analysis: theory, methods applications 69, No. 11, 3877-3896 (2008) · Zbl 1169.34006 · doi:10.1016/j.na.2007.10.021
[23]Babakhani, A.; Baleanu, D.: Employing of some basic theory for class of fractional differential equations, Advances in difference equations 2011 (2011)