More properties of the proportional fractional integrals and derivatives of a function with respect to another function
Fahd Jarad, Thabet Abdeljawad, Saima Rashid, Zakia Hammouch
Abstract
Abstract In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann–Liouville setting and the one in Caputo. In addition, we provide an integration by parts formulas related to the considered operators.
Topics & Concepts
MathematicsLaplace transformFunction (biology)Fractional calculusMittag-Leffler functionOrdinary differential equationApplied mathematicsGreen's function for the three-variable Laplace equationPartial differential equationMathematical analysisInverse Laplace transformDifferential equationBiologyEvolutionary biologyFractional Differential Equations SolutionsMathematical Inequalities and ApplicationsIterative Methods for Nonlinear Equations