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- W2941664585 abstract "In this thesis, new and effective operational methods based on polynomials andwavelets for the solutions of FDEs and systems of FDEs are developed. In particularwe study one of the important polynomial that belongs to the Appell family ofpolynomials, namely, Genocchi polynomial. This polynomial has certain greatadvantages based on which an effective and simple operational matrix of derivativewas first derived and applied together with collocation method to solve some singularsecond order differential equations of Emden-Fowler type, a class of generalizedPantograph equations and Delay differential systems. A new operational matrix offractional order derivative and integration based on this polynomial was alsodeveloped and used together with collocation method to solve FDEs, systems ofFDEs and fractional order delay differential equations. Error bound for some of theconsidered problems is also shown and proved. Further, a wavelet bases based onGenocchi polynomials is also constructed, its operational matrix of fractional orderderivative is derived and used for the solutions of FDEs and systems of FDEs. Anovel approach for obtaining operational matrices of fractional derivative based onLegendre and Chebyshev wavelets is developed, where, the wavelets are firsttransformed into corresponding shifted polynomials and the transformation matricesare formed and used together with the polynomials operational matrices of fractionalderivatives to obtain the wavelets operational matrix. These new operational matricesare used together with spectral Tau and collocation methods to solve FDEs andsystems of FDEs." @default.
- W2941664585 created "2019-05-03" @default.
- W2941664585 creator A5046410968 @default.
- W2941664585 date "2017-02-01" @default.
- W2941664585 modified "2023-09-26" @default.
- W2941664585 title "Wavelets operational methods for fractional differential equations and systems of fractional differential equations" @default.
- W2941664585 hasPublicationYear "2017" @default.
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