TY - JOUR
ID - 6349
TI - Application of Shannon wavelet for solving boundary value problems of fractional differential equations I
JO - Wavelet and Linear Algebra
JA - WALA
LA - en
SN - 2383-1936
AU - Nouri, K.
AU - Bahrami Siavashani, N.
AD - School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box:
19395-5746, Tehran, Islamic Republic of Iran
AD - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences,
Semnan University, P. O. Box: 35195-363, Semnan, Islamic Republic of Iran.
Y1 - 2014
PY - 2014
VL - 1
IS - 1
SP - 33
EP - 42
KW - Boundary value problems
Fractional differential
equations
Shannon wavelet
Operational matrix
DO -
N2 - Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. Therefore, a reliable and efficient technique as a solution is regarded. This paper develops approximate solutions for boundary value problems of differential equations with non-integer order by using the Shannon wavelet bases. Wavelet bases have different resolution capability for approximating of different functions. Since for Shannon-type wavelets, the scaling function and the mother wavelet are not necessarily absolutely integrable, the partial sums of the wavelet series behave differently and a more stringent condition, such as bounded variation, is needed for convergence of Shannon wavelet series. With nominate Shannon wavelet operational matrices of integration, the solutions are approximated in the form of convergent series with easily computable terms. Also, by applying collocation points the exact solutions of fractional differential equations can be achieved by well-known series solutions. Illustrative examples are presented to demonstrate the applicability and validity of the wavelet base technique. To highlight the convergence, the numerical experiments are solved for different values of bounded series approximation.
UR - https://wala.vru.ac.ir/article_6349.html
L1 - https://wala.vru.ac.ir/article_6349_a879aab68ceb63c1143db65fbc4b6bc7.pdf
ER -