000 04210nam a22005055i 4500
001 978-1-4614-4036-9
003 DE-He213
005 20140220083249.0
007 cr nn 008mamaa
008 120816s2012 xxu| s |||| 0|eng d
020 _a9781461440369
_9978-1-4614-4036-9
024 7 _a10.1007/978-1-4614-4036-9
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aAbbas, Saïd.
_eauthor.
245 1 0 _aTopics in Fractional Differential Equations
_h[electronic resource] /
_cby Saïd Abbas, Mouffak Benchohra, Gaston M. N'Guérékata.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2012.
300 _aXIII, 396 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aDevelopments in Mathematics,
_x1389-2177 ;
_v27
505 0 _aPreface -- 1. Preliminary Background -- 2. Partial Hyperbolic Functional Differential Equations -- 3. Partial Hyperbolic Functional Differential Inclusions -- 4. Impulsive Partial Hyperbolic Functional Differential Equations -- 5. Impulsive Partial Hyperbolic Functional Differential Inclusions -- 6. Implicit Partial Hyperbolic Functional Differential Equations -- 7. Fractional Order Riemann-Liouville Integral Equations -- References -- Index.
520 _aDuring the last decade, there has been an explosion of interest in fractional dynamics as it was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media. Fractional calculus generalizes integrals and derivatives to non-integer orders and has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. This book is addressed to a wide audience of researchers working with fractional dynamics, including mathematicians, engineers, biologists, and physicists. This timely publication may also be suitable for a graduate level seminar for students studying differential equations.   Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. In this book, problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. An historical introduction to fractional calculus will be of general interest to a wide range of researchers. Chapter one contains some preliminary background results. The second Chapter is devoted to fractional order partial functional differential equations. Chapter three is concerned with functional partial differential inclusions, while in the fourth chapter, we consider functional impulsive partial hyperbolic differential equations. Chapter five is concerned with impulsive partial hyperbolic functional differential inclusions. Implicit partial hyperbolic differential equations are considered in Chapter six, and finally in Chapter seven, Riemann-Liouville fractional order integral equations are considered. Each chapter concludes with a section devoted to notes and bibliographical remarks. The work is self-contained but also contains questions and directions for further research.
650 0 _aMathematics.
650 0 _aFunctional equations.
650 0 _aIntegral equations.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aIntegral Equations.
650 2 4 _aDifference and Functional Equations.
700 1 _aBenchohra, Mouffak.
_eauthor.
700 1 _aN'Guérékata, Gaston M.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461440352
830 0 _aDevelopments in Mathematics,
_x1389-2177 ;
_v27
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-4036-9
912 _aZDB-2-SMA
999 _c101474
_d101474