THE CALCULUS OF BIVARIATE FRACTAL INTERPOLATION SURFACES
SUBHASH CHANDRA, SYED ABBAS
Abstract
In this paper, we investigate partial integrals and partial derivatives of bivariate fractal interpolation functions (FIFs). We also prove that the mixed Riemann–Liouville fractional integral and derivative of order [Formula: see text], of bivariate FIFs are again bivariate interpolation functions corresponding to some iterated function system (IFS). Furthermore, we discuss the integral transforms and fractional order integral transforms of the bivariate FIFs.
Topics & Concepts
MathematicsBivariate analysisInterpolation (computer graphics)Iterated function systemFractional calculusFractalPartial derivativeApplied mathematicsMathematical analysisOrder (exchange)Iterated functionPure mathematicsCalculus (dental)Function (biology)Multiple integralTrigonometric interpolationDerivative (finance)Bilinear interpolationNearest-neighbor interpolationRiemann integralMathematical Dynamics and FractalsAnalytic and geometric function theoryMathematical functions and polynomials