INTEGRAL TRANSFORM METHOD FOR SOLVING DIFFERENT F.S.I.ES AND P.F.D.ES

INTEGRAL TRANSFORM METHOD FOR SOLVING DIFFERENT F.S.I.ES AND P.F.D.ES

In this work, the authors used Laplace transform to obtain formalsolution to some systems of singular integral equations of fractional type. Inthe last section, the authors considered certain non homogeneous fractionalsystem of heat equations with different orders which is a generalization to theproblem of heat transferring from metallic bar through the surrounding media.Illustrative examples are also provided

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  • Aghili, A., Ansari, A. Solving partial fractional differential equations using the LA- transform. Asian-European journal of mathematics. Vol 3, No 2, 209-220, 2010.
  • Aghili, A., Masomi, M.R. Solution to time fractional partial differential equations and dynamical systems via integral transforms. Journal of Interdisciplinary Mathematics. Vol 14, Issue 5-6, 545-560, 2011.
  • Aghili, A., Masomi, M.R. Solution to time fractional partial differential equations via joint Laplace-Fourier transforms. Journal of Interdisciplinary Mathematics Volume 15, Issue 2-3, 121-135, 2012.
  • Aghili, A., Masomi, M.R. Integral transform method for solving time fractional systems and fractional heat equation. Boletim da Sociedade Paranaense de Matemtica, Vol 32, No 1, pp 305-322, 2014.
  • Aghili, A., Masomi, M.R. Transform method for solving time-fractional order systems of nonlinear differential and difference equations. Antarctica J. Math., 10(3), 237-251, 2013.
  • Aghili, A., Masomi, M.R. The double Post-Widder inversion formula for two dimensional Laplace transform and Stieltjes transform with applications. Bulletin of Pure and Applied Sciences, Volume 30 E (Math and Stat.) Issue 2, 191-204, 2011.
  • Aghili, A., Salkhordeh Moghaddam, B. Laplace transform pairs of N-dimensions and second order linear partial differential equations with constant coefficients. Annales Mathematicae et Informaticae 35, 310, 2008.
  • Bobylev, A.V., Cercignani, C. The inverse Laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation. Appl. Math. Lett. 15, 807-813, 2002.
  • Ditkin, V.A., Prudnikov, A.P. Calcul operationnelle. Mir publisher. 1979.
  • Duffy, D.G. Transform methods for solving partial differential equations. Chapman and Hall/CRC, 2004.
  • Kartashov, E.M., Lyubov, B.Ya., Bartenev, G.M. A diffusion problem in a region with a moving boundary. Soviet Physics Journal, Vol 13, Issue 12, 1641-1647, 1970.
  • Kilbas, A.A., Srivastava, H.M., Trujillo, J.J. Theory and applications of fractional differential equations. Elsevier, 2006.
  • Langlands T. Solution of a modified fractional diffusion equation. Physica A, 367, 136-144, 2006.
  • Liu, F., Anh, V.V., Turner, I., Zhuang, P. Time fractional advection dispersion equation. Appl. Math. Computing, 13, 233-245, 2003.
  • Minardi, F., Pagnini, G. The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Comput. Appl. Math. Vol 207, Issue 2, 245-257, 2007.
  • Minardi, F., Pagnini, G. The Wright functions as solutions of the time fractional diffusion equations. Appl. Math. Comput. Vol 141, Issue 1, 51-62, 2003.
  • Minardi, F., Pagnini, G., Gorenflo, R. Some aspects of fractional diffusion equations of single and distributed order. J. Comput. Appl. Math. Vol 187, Issue 1, 295-305, 2007.
  • Mainardi, F., Pagnini, G., Saxena, R. K. Fox H-functions in fractional diffusion. J. Comput. Appl. Math. 178, 321-331, 2005.
  • Podlubny, I. Fractional differential equations. Academic Press, 1999.
  • Redozubov, D.B. The Solution of linear thermal problems with a uniformly moving boundary in a sSemiinfinite region. Sov. Phys. Tech. Phys., 5, 570574, 1960.
  • Saichev, A., Zaslavsky, G. Fractional kinetic equations: solutions and applications. Chaos. 7(4), 753-764, 1997.
  • Saxena, R.K., Mathai, A.M., Haubold, H.J. Solutions of certain fractional kinetic equations and a fractional diffusion equation. Math. Phys. 51, 103506, 2010.
  • Sneddon, I. Ulam, S. Stark, M. Operational Calculus in two variables and its applications. Pergamon Press Ltd, 1962.
  • Wyss, W. The fractional diffusion equation. Math. Phys. 27, 2782-2785, 1986.
  • Yu, R., Zhang, H. New function of Mittag-Leffler type and its application the fractional diffusion-wave equation. Chaos, Solitons Fract. Vol 30, Issue 4, 946-955, 2006.
  • Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan. P.O. Box, 1841, Rasht - Iran
  • E-mail address: armanaghili@yahoo.com , masomirasool@yahoo.com