Solution to linear KdV and nonLinear space fractional PDEs
Resumo
In this work, the author will briefly discuss applications of the Fourier and Laplace transforms in the solution of certain singular integral equations and evaluation of integrals. By combining integral transforms and operational methods we get more powerful analytical tool for solving a wide class of linear or even non- linear fractional differential or fractional partial differential equation. Numerous examples and exercises occur throughout the paper.
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Referências
A. Aghili. Solution to time fractional Couette flow. TWMS J. App. Eng. Math. V.8, N.2, 2018.
A. Aghili, H. Zeinali, Advances in Laplace type integral transforms with applications, Indian Journal of Science and Technology, Vol. 7(6)2014, 877–890.
A. Ansari. Fractional exponential operators and nonlinear partial fractional differential equations in the Weyl fractional derivatives, Applied Mathematics and Computation 220, 149-154 2013.
A. Ansari.Some inverse fractional Legendre transforms of gamma function form, Kodai Mathematical Journal 38 (3), 658-671 2015.
A. Ansari. Remarks on Green function of space-fractional biharmonic heat equation using Ramanujan’s master theorem, Kuwait Journal of Science 44 (4) 2017.
A. Apelblat, Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
G. Dattoli, H. M. Srivastava, K. V. Zhukovsky. Operational methods and differential equations to initial value problems. Applied Mathematics and computations.184 (2007) pp 979-1001.
G. Dattoli, P. L. Ottaviani, A. Torre, L. Vazquez, Evolution operator equations: integration with algebraic and finitedifference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory,La Rivista del Nuovo Cimento 20 (1997) 2.pp. 1-132.
B. Davies, Integral transforms and their applications, New York: Springer- Verlag 2007.
I. Podlubny., Fractional Differential Equations, Academic Press, San Diego, CA,1999.
O. Vallee, M. Soares. Airy Functions and Applications to Physics. London: Imperial College Press; 2004.
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