Fractional Calculus of the Extended Hypergeometric Function
Recep Şahіn, Oğuz Yağcı
Abstract
Abstract Here, our aim is to demonstrate some formulae of generalization of the extended hypergeometric function by applying fractional derivative operators. Furthermore, by applying certain integral transforms on the resulting formulas and develop a new futher generalized form of the fractional kinetic equation involving the generalized Gauss hypergeometric function. Also, we obtain generating functions for generalization of extended hypergeometric function..
Topics & Concepts
Generalized hypergeometric functionConfluent hypergeometric functionHypergeometric function of a matrix argumentMathematicsGeneralizationHypergeometric functionBasic hypergeometric seriesHypergeometric identityBilateral hypergeometric seriesFractional calculusBarnes integralLauricella hypergeometric seriesPure mathematicsGaussFunction (biology)Algebra over a fieldMathematical analysisApplied mathematicsPhysicsBiologyEvolutionary biologyQuantum mechanicsFractional Differential Equations SolutionsMathematical functions and polynomialsIterative Methods for Nonlinear Equations