Fractional Differential Equations > http://shurll.com/9fg2h

Fractional Differential Equations


1f3b4efedd
21952201…(October…2011)…^…S….Geophys..Repeating.this.gives.the.more.general.result.that…..Proof..(..J..α..)..(..J..β..f..)..(..x..)..=..1..Γ..(..α..)..∫..0..x..(..x..−..t..)..α..−..1..(..J..β..f..)..(..t..)..d..t..=..1..Γ..(..α..)..Γ..(..β..)..∫..0..x..∫..0..t..(..x..−..t..)..α..−..1..(..t..−..s..)..β..−..1..f..(..s..)..d..s..d..t..=..1..Γ..(..α..)..Γ..(..β..)..∫..0..x..f..(..s..)..(..∫..s..x..(..x..−..t..)..α..−..1..(..t..−..s..)..β..−..1..d..t..)..d..s..{displaystyle..{begin{aligned}(J^{alpha..})(J^{beta..}f)(x)&={frac..{1}{Gamma..(alpha..)}}int..{0}^{x}(x-t)^{alpha..-1}(J^{beta..}f)(t);dt&={frac..{1}{Gamma..(alpha..)Gamma..(beta..)}}int..{0}^{x}int..{0}^{t}(x-t)^{alpha..-1}(t-s)^{beta..-1}f(s);ds;dt&={frac..{1}{Gamma..(alpha..)Gamma..(beta..)}}int..{0}^{x}f(s)left(int..{s}^{x}(x-t)^{alpha..-1}(t-s)^{beta..-1};dtright)dsend{aligned}}}..where..in..the..last..step..we..exchanged..the..order..of..integration..and..pulled..out..the..f(s)..factor..from..the..t..integration…Mainardi,…"Fractional…Diffusion…Processes:…Probability…Distributions…and…Continuous…Time…Random…Walk",…Springer…Lecture…Notes…in…Physics,…No…621,…Berlin…2003,…pp….For…negative…integer…power…k,…the…gamma…function…is…undefined…and…we…have…to…use…the…following…relation:[2]….Biol.,..40(4),..pp…Fractional…Dynamics:…Applications…of…Fractional…Calculus…to…Dynamics…of…Particles,…Fields…and…Media….

Debnath,…L….M.D….n..=..⌈..α..⌉..{displaystyle..n=lceil..alpha..rceil..}…..Let…us…assume…that…f(x)…is…a…monomial…of…the…form….The.numerical.simulations.showed.that,.the.modified.equation.is.more.reliable.in.predicting.the.movement.of.pollution.in.the.deformable.aquifers,.than.the.constant.fractional.and.integer.derivatives[15]..In..applied..mathematics..and..mathematical..analysis,..fractional..derivative..is..a..derivative..of..any..arbitrary..order,..real..or..complex…This..equation..has..been..shown..useful..for..modeling..contaminant..flow..in..heterogenous..porous..media.[12][13][14]..Atangana..and..Kilicman..extended..fractional..advection..dispersion..equation..to..variable..order..fractional..advection..dispersion..equation…

sperma diat fur speck fotzenMicrosoft Office 2011 14.2.3 Serial for Mac ( Keygensoftwarezator 2012 - Full Downloadaaliyah-by-aaliyah_rarSpore_No_PasswordProgramul_Chestionare_Auto_Home_Edition_2.0Hunting Unlimited (2011/ENG/RePack by Ultra)Tomba_2_Iso_PsxProduct_Code_For_Fifa_12_OriginShadow The Hedgehog - All Hail Shadow!