Search results for "Fractional differentiation"

showing 3 items of 3 documents

Fractional integration, differentiation, and weighted Bergman spaces

1999

We study the action of fractional differentiation and integration on weighted Bergman spaces and also the Taylor coeffficients of functions in certain subclasses of these spaces. We then derive several criteria for the multipliers between such spaces, complementing and extending various recent results. Univalent Bergman functions are also considered.

Pure mathematicsMathematics::Complex VariablesGeneral Mathematics010102 general mathematicsMathematical analysisMathematical statisticsTaylor coefficientsMathematics & Statistics01 natural sciencesAction (physics)010101 applied mathematicsFractional differentiationBergman space0101 mathematicsMathematicsBergman kernel
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Experimental demonstration of fractional order differentiation using a long-period grating-based in-fiber modal interferometer

2016

In this work we demonstrate both, experimentally and theoretically, that a long-period grating-based in-fiber modal interferometer can perform an all-optical arbitrary-order fractional differentiation. Experimentally, we fractionally differentiated to the 0.5th order a secant hyperbolic-like pulse of 23 ps time width provided by a 1039.5 nm emission wavelength modelocked fiber laser, with a chirp parameter of −30. An analytical expression relating the fractional order of differentiation n with the characteristics of the modal interferometer was also derived, with the purpose to simplify the design procedure. The proposal was corroborated also numerically. This device may find applications i…

Optical fiberCiencias FísicasPhase (waves)Physics::Optics02 engineering and technologyGratingMach–Zehnder interferometer01 natural sciencesFRACTIONAL DIFFERENTIATIONlaw.invention010309 optics020210 optoelectronics & photonicsOpticslawFiber laser0103 physical sciences0202 electrical engineering electronic engineering information engineeringChirpElectrical and Electronic EngineeringPhysical and Theoretical ChemistryFIBER OPTICSPhysicsbusiness.industryAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsPulse (physics)AstronomíaWavelengthLONG-PERIOD GRATINGbusinessMACH–ZEHNDERCIENCIAS NATURALES Y EXACTASOptics Communications
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Long-period grating assisted fractional differentiation of highly chirped light pulses

2016

We experimentally demonstrate the possibility to perform a fractional differentiation of arbitrary order on a given light pulse by propagation through a single long-period grating. A simple analytical expression is obtained also, relating the fractional order of differentiation with the parameters of the long-period grating. A secant hyperbolic like pulse of 23 ps time width with a chirp parameter of -30 was successfully fractionally differentiated to the 0.5th order. The proposal was corroborated experimentally and numerically. The device may find applications in real time phase recovery. Fil: Poveda Wong, L.. Universidad de Valencia; España Fil: Carrascosa, A.. Universidad de Valencia; Es…

Ciencias FísicasPhase (waves)02 engineering and technologyGratingOtras Ciencias Físicas01 natural sciences010309 opticsFractional differentiation020210 optoelectronics & photonicsOpticsLong period0103 physical sciences0202 electrical engineering electronic engineering information engineeringChirpPULSE SHAPINGElectrical and Electronic EngineeringPhysical and Theoretical ChemistryOPTICAL PROCESSINGPhysicsbusiness.industryOptical processingALL-OPTICAL DEVICESPulse shapingAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsPulse (physics)businessCIENCIAS NATURALES Y EXACTAS
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