Real and complex order integrals and derivatives operators over the set of causal functions

2013/02/14 by Raoelina Andriambololona, Andriambololona, Raoelina
Engineering · Mathematics · #Advanced Control Systems Design #Fractional Differential Equations Solutions #Mathematical Inequalities and Applications #math.GM

paper · pdf · doi:10.48550/arxiv.1302.4711

8 pages

arxiv created 2013/02/14 · arxiv updated 2013/02/20

Abstract

The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives definition is derived from fractional integrals one. Then an unified definition of fractional integrals and derivatives operator is obtained according to the sign of the real part of the order s. The study utilizes many properties of the Euler's gamma and beta functions and their extensions in R and C. Comparison with the definitions given by other authors (Liouville, Riemann,Liouville-Caputo)is done too.

Related

• A new operator giving integrals and derivatives operators for any order at the same time
• Derivatives and integrals: matrix order operators as an extension of the fractional calculus
• About Fractional Calculus and its Applications in Physics
• On new types of fractional operators and applications
• Fractional Derivatives: an extension of classical analysis to non-integer orders