2019
DOI: 10.1016/j.cam.2018.09.040
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Numerical solution based on hybrid of block-pulse and parabolic functions for solving a system of nonlinear stochastic Itô–Volterra integral equations of fractional order

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Cited by 41 publications
(17 citation statements)
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“…There are many definitions for fractional integral and fractional derivative. Among them, the Riemann‐Liouville definition usually is used for fractional integral, whereas the Caputo definition is frequently applied for fractional derivative …”
Section: Preliminaries and Initial Definitionsmentioning
confidence: 99%
See 1 more Smart Citation
“…There are many definitions for fractional integral and fractional derivative. Among them, the Riemann‐Liouville definition usually is used for fractional integral, whereas the Caputo definition is frequently applied for fractional derivative …”
Section: Preliminaries and Initial Definitionsmentioning
confidence: 99%
“…Among them, the Riemann-Liouville definition usually is used for fractional integral, whereas the Caputo definition is frequently applied for fractional derivative. [20][21][22][23][24][25] Definition 4. The Riemann-Liouville fractional integral operator of order is defined as follows:…”
Section: Fractional Calculusmentioning
confidence: 99%
“…Maleknejad and Mahmoudi used hybrid of BPFs and Taylor polynomials (HBT) to numerically solve linear Fredholm integral equation in [20]. Mirzaee et al proposed a method based on hybrid of BPFs and parabolic functions for solving a system of nonlinear stochastic Itô-Volterra integral equations of fractional order in [21]. Jafari Behbahani and Roodaki introduced a combination of Chebyshev polynomials and BPFs to seek the numerical solution of integral equations in [22].…”
Section: Introductionmentioning
confidence: 99%
“…Both mathematicians and physicists have devoted considerable effort to find robust and stable analytical and numerical methods for solving stochastic differential equations, Adomian method [2], implicit Taylor methods [3,4] and recently the operational matrices ofintegration for orthogonal polynomials Legendre wavelets, Chebyshev polynomials, etc. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Several analytical and numerical methods have been proposed for solving various types of stochastic problems with the classical Brownian motion [10,12,14,[21][22][23].…”
Section: Introductionmentioning
confidence: 99%