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)
Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets. (English) Zbl 1221.65140
Summary: A computational method for numerical solution of a nonlinear Volterra integro-differential equation of fractional (arbitrary) order which is based on CAS wavelets and BPFs is introduced. The CAS wavelet operational matrix of fractional integration is derived and used to transform the main equation to a system of algebraic equations. Some examples are included to demonstrate the validity and applicability of the technique.

65J20Improperly posed problems; regularization (numerical methods in abstract spaces)
65R20Integral equations (numerical methods)
26A33Fractional derivatives and integrals (real functions)
45J05Integro-ordinary differential equations
65T60Wavelets (numerical methods)
Full Text: DOI
[1] Caputo, M.: Linear models of dissipation whose Q is almost frequency independent -- II, Geophys J royal astron soc 13, 529539 (1967)
[2] Mainardi, F.: Fractional calculus: some basic problems in continuum and statistical mechanics, Fractals and fractional calculus in continuum mechanics, 291348 (1997) · Zbl 0917.73004
[3] Olmstead, W.; Handelsman, R.: Diffusion in a semi-infinite region with nonlinear surface dissipation, SIAM rev 18, 275291 (1976) · Zbl 0323.45008 · doi:10.1137/1018044
[4] Momani, S.: Local and global existence theorems on fractional integro-differential equations, J fract calculus 18, 8186 (2000) · Zbl 0967.45004
[5] Rawashdeh, E. A.: Numerical solution of fractional integro-differential equations by collocation method, Appl math comput 176, 1-6 (2006) · Zbl 1100.65126 · doi:10.1016/j.amc.2005.09.059
[6] Boyadjiev, L.; Dobner, H. J.; Kalla, S. L.: A fractional integro-differential equation of Volterra type, Math comput modell 28, 103-113 (1998) · Zbl 0993.65153 · doi:10.1016/S0895-7177(98)00158-7
[7] Nazari D, Shahmorad S. Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions. J Comput Appl Math. doi:10.1016/j.cam.2010.01.053. · Zbl 1188.65174
[8] Arikoglu, A.; Ozkol, I.: Solution of fractional integro-differential equations by using fractional differential transform method, Chaos solitons fract 40, 521-529 (2009) · Zbl 1197.45001 · doi:10.1016/j.chaos.2007.08.001
[9] Momani, S.; Qaralleh, R.: An efficient method for solving systems of fractional integro-differential equations, Comput math appl 52, 459-470 (2006) · Zbl 1137.65072 · doi:10.1016/j.camwa.2006.02.011
[10] Boyadjiev, L.; Kalla, S. L.; Khajah, H. G.: Analytical and numerical treatment of a fractional integro-differential equation of Volterra type, Math comput modell 25, 1-9 (1997) · Zbl 0932.45012 · doi:10.1016/S0895-7177(97)00090-3
[11] Saberi-Nadjafi, J.; Ghorbani, A.: He’s homotopy perturbation method: an effective tool for solving nonlinear integral and integro-differential equations, Comput math appl 58, 23792390 (2009) · Zbl 1189.65173 · doi:10.1016/j.camwa.2009.03.032
[12] Kilicman, A.; Zhour, Z. A. A. Al: Kronecker operational matrices for fractional calculus and some applications, Appl math comput 187, No. 1, 25065 (2007) · Zbl 1123.65063 · doi:10.1016/j.amc.2006.08.122
[13] Momani, S.; Noor, M.: Numerical methods for fourth order fractional integro-differential equations, Appl math comput 182, 754-760 (2006) · Zbl 1107.65120 · doi:10.1016/j.amc.2006.04.041
[14] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[15] Rao, C. R.: Piecewise orthogonal functions and their applications on system and control, (1983)