Memory Effects in Diffusion Like Equation Via Haar Wavelets

Youssef, I. K.

doi:10.11648/j.pamj.20160504.17

Cited by 4 publications

(9 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The technique is described in many publications [6,14,15] and the references cited there. The Haar wavelet family, ℎ % ( ); 0 ≤ ≤ 1 is used as bases and are defined as:…”

Section: Haar Waveletsmentioning

confidence: 99%

“…Wavelet analysis allows representing a function or signal in terms of a set of orthonormal basis functions called wavelets. Haar wavelets are a basis for @ 5 [0, 1], for more details you can see [6] and the references there in.…”

Section: Haar Waveletsmentioning

confidence: 99%

“…with " = 2 8 + 9, 0 ≤ :, and 0 ≤ 9 < 2 8 , [6]. Generally, the series in (8) can be truncated to a finite number of terms.…”

Section: Function Approximationmentioning

confidence: 99%

“…In [5] Youssef and Shukur use the modified variational iteration method to construct an approximate solution to a fractional time and space diffusion equation. In [6] the authors considered the memory effects due to the existence of fractional time derivatives and a time dependent integral term via Haar wavelets treatment in the form…”

Section: Introductionmentioning

confidence: 99%

“…As our treatment in [6] the fractional derivatives appears in equation (2) can be translated to the right hand side as…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets

Youssef¹

2016

ACM

Self Cite

View full text Add to dashboard Cite

Abstract:Memory and hereditary effects due to fractional time derivative are combined with the global behaviours due to space integral term. Haar wavelet operational matrix is adjusted to solve diffusion like equations with time fractional derivative, space derivatives and integral terms. The fractional derivative is understood in the Caputo sense. The memory behaviours is included in all the points of the domain due to the existence of space integral term and the inverse fractional operator treatment and this is ilustrated in error graphs introduced. A general example with four subproblems ranging from the simple classical heat equation to the fractional time diffusion equation with global integral term is proposed and the calculated results are displayed graphically.

show abstract

“…The technique is described in many publications [6,14,15] and the references cited there. The Haar wavelet family, ℎ % ( ); 0 ≤ ≤ 1 is used as bases and are defined as:…”

Section: Haar Waveletsmentioning

confidence: 99%

Section: Haar Waveletsmentioning

confidence: 99%

“…with " = 2 8 + 9, 0 ≤ :, and 0 ≤ 9 < 2 8 , [6]. Generally, the series in (8) can be truncated to a finite number of terms.…”

Section: Function Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…As our treatment in [6] the fractional derivatives appears in equation (2) can be translated to the right hand side as…”

Section: Introductionmentioning

confidence: 99%