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A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS
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| Zeitschriftentitel: | The ANZIAM Journal |
|---|---|
| Personen und Körperschaften: | |
| In: | The ANZIAM Journal, 55, 2013, 1, S. 69-92 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Cambridge University Press (CUP)
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| Schlagwörter: |
| author_facet |
KHADER, M. M. KHADER, M. M. |
|---|---|
| author |
KHADER, M. M. |
| spellingShingle |
KHADER, M. M. The ANZIAM Journal A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS Mathematics (miscellaneous) |
| author_sort |
khader, m. m. |
| spelling |
KHADER, M. M. 1446-1811 1446-8735 Cambridge University Press (CUP) Mathematics (miscellaneous) http://dx.doi.org/10.1017/s1446181113000321 <jats:title>Abstract</jats:title><jats:p>A new formula for Adomian polynomials is introduced and applied to obtain truncated series solutions for fractional initial value problems with nondifferentiable functions. These kinds of equations contain a fractional single term which is examined using Jumarie fractional derivatives and fractional Taylor series for nondifferentiable functions. The property of nonlocality of these equations is examined, and the existence and uniqueness of solutions are discussed. Convergence and error analysis for the Adomian series solution are also studied. Numerical examples show the accuracy and efficiency of this formula for solving initial value problems for high-order fractional differential equations.</jats:p> A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS The ANZIAM Journal |
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A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_unstemmed |
A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_full |
A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_fullStr |
A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_full_unstemmed |
A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_short |
A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_sort |
a new formula for adomian polynomials and the analysis of its truncated series solution for fractional non-differentiable initial value problems |
| topic |
Mathematics (miscellaneous) |
| url |
http://dx.doi.org/10.1017/s1446181113000321 |
| publishDate |
2013 |
| physical |
69-92 |
| description |
<jats:title>Abstract</jats:title><jats:p>A new formula for Adomian polynomials is introduced and applied to obtain truncated series solutions for fractional initial value problems with nondifferentiable functions. These kinds of equations contain a fractional single term which is examined using Jumarie fractional derivatives and fractional Taylor series for nondifferentiable functions. The property of nonlocality of these equations is examined, and the existence and uniqueness of solutions are discussed. Convergence and error analysis for the Adomian series solution are also studied. Numerical examples show the accuracy and efficiency of this formula for solving initial value problems for high-order fractional differential equations.</jats:p> |
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| description | <jats:title>Abstract</jats:title><jats:p>A new formula for Adomian polynomials is introduced and applied to obtain truncated series solutions for fractional initial value problems with nondifferentiable functions. These kinds of equations contain a fractional single term which is examined using Jumarie fractional derivatives and fractional Taylor series for nondifferentiable functions. The property of nonlocality of these equations is examined, and the existence and uniqueness of solutions are discussed. Convergence and error analysis for the Adomian series solution are also studied. Numerical examples show the accuracy and efficiency of this formula for solving initial value problems for high-order fractional differential equations.</jats:p> |
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| spelling | KHADER, M. M. 1446-1811 1446-8735 Cambridge University Press (CUP) Mathematics (miscellaneous) http://dx.doi.org/10.1017/s1446181113000321 <jats:title>Abstract</jats:title><jats:p>A new formula for Adomian polynomials is introduced and applied to obtain truncated series solutions for fractional initial value problems with nondifferentiable functions. These kinds of equations contain a fractional single term which is examined using Jumarie fractional derivatives and fractional Taylor series for nondifferentiable functions. The property of nonlocality of these equations is examined, and the existence and uniqueness of solutions are discussed. Convergence and error analysis for the Adomian series solution are also studied. Numerical examples show the accuracy and efficiency of this formula for solving initial value problems for high-order fractional differential equations.</jats:p> A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS The ANZIAM Journal |
| spellingShingle | KHADER, M. M., The ANZIAM Journal, A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS, Mathematics (miscellaneous) |
| title | A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_full | A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_fullStr | A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_full_unstemmed | A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_short | A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| title_sort | a new formula for adomian polynomials and the analysis of its truncated series solution for fractional non-differentiable initial value problems |
| title_unstemmed | A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS |
| topic | Mathematics (miscellaneous) |
| url | http://dx.doi.org/10.1017/s1446181113000321 |