New results on complex conformable integral
Francisco Martínez, Inmaculada Martínez, Mohammed K. A. Kaabar, Silvestre Paredes
Abstract
<abstract> A new theory of analytic functions has been recently introduced in the sense of conformable fractional derivative. In addition, the concept of fractional contour integral has also been developed. In this paper, we propose and prove some new results on complex fractional integration. First, we establish necessary and sufficient conditions for a continuous function to have antiderivative in the conformable sense. Finally, some of the well-known Cauchy′s integral theorems will also be the subject of the extension that we do in this paper. </abstract>
Topics & Concepts
Conformable matrixExtension (predicate logic)Fractional calculusCauchy's integral formulaMethods of contour integrationMathematicsFunction (biology)Calculus (dental)Integration by partsApplied mathematicsPure mathematicsMathematical analysisComputer scienceCauchy problemInitial value problemPhysicsQuantum mechanicsEvolutionary biologyBiologyDentistryProgramming languageMedicineFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisFunctional Equations Stability Results