An analytical study on Mittag‐Leffler–confluent hypergeometric functions with fractional integral operator

F. Ghanim, Hiba F. Al‐Janaby

2020Mathematical Methods in the Applied Sciences33 citationsDOI

Abstract

The Mittag‐Leffler function (M‐LF) and confluent hypergeometric function were first created in relation to the interpolation problem for the exponential function. During the 20th century, the gamma function was used to introduce many formulations of these functions. Further investigation in this theme led various scholars to research numerous implementations in applied sciences and other allied disciplines. Recently, the interest in M‐LF has significantly developed and a variety of extensions and generalizations forms have been posed. In this research, we define and study a new function called Mittag‐Leffler–confluent hypergeometric function (MLCHF). Moreover, we examine the integral equations with several analytic implementations.

Topics & Concepts

MathematicsConfluent hypergeometric functionHypergeometric functionMittag-Leffler functionSpecial functionsGeneralized hypergeometric functionBasic hypergeometric seriesFunction (biology)Hypergeometric identityAlgebra over a fieldHypergeometric function of a matrix argumentInterpolation (computer graphics)Exponential functionOperator (biology)Pure mathematicsGamma functionFractional calculusApplied mathematicsMathematical analysisComputer scienceTranscription factorAnimationEvolutionary biologyChemistryGeneBiologyRepressorBiochemistryComputer graphics (images)Fractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsMathematical functions and polynomials