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200 10$aErdélyi?Kober Fractional Calculus $eFrom a Statistical Perspective, Inspired by Solar Neutrino Physics /$fby A. M. Mathai, H. J. Haubold
205   $a1st ed. 2018.
210  1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2018.
215   $a1 online resource (XII, 122 p. 6 illus., 3 illus. in color.) 
225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v31
311   $a981-13-1158-7 
330   $aThis book focuses on Erdélyi?Kober fractional calculus from a statistical perspective inspired by solar neutrino physics. Results of diffusion entropy analysis and standard deviation analysis of data from the Super-Kamiokande solar neutrino experiment lead to the development of anomalous diffusion and reaction in terms of fractional calculus. The new statistical perspective of Erdélyi?Kober fractional operators outlined in this book will have fundamental applications in the theory of anomalous reaction and diffusion processes dealt with in physics. A major mathematical objective of this book is specifically to examine a new de?nition for fractional integrals in terms of the distributions of products and ratios of statistically independently distributed positive scalar random variables or in terms of Mellin convolutions of products and ratios in the case of real scalar variables. The idea will be generalized to cover multivariable cases as well as matrix variable cases. In the matrix variable case, M-convolutions of products and ratios will be used to extend the ideas. We then give a de?nition for the case of real-valued scalar functions of several matrices.
410  0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v31
606   $aMathematical physics
606   $aSpecial functions
606   $aFunctional analysis
606   $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000
606   $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
615  0$aMathematical physics.
615  0$aSpecial functions.
615  0$aFunctional analysis.
615 14$aMathematical Physics.
615 24$aSpecial Functions.
615 24$aFunctional Analysis.
676   $a530.15
700   $aMathai$b A. M$4aut$4http://id.loc.gov/vocabulary/relators/aut$0441283
702   $aHaubold$b H. J$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910349474203321
996   $aErdélyi?Kober Fractional Calculus$92129310
997   $aUNINA