On Fractional φ- and biφ-calculi

Abstract

In this paper we introduce fractional φ- and biφ-calculi using Riemann-Liouville approach and Caputo approach as well. An effort is put into explaining the basic principles of these calculi since they are not as common as classical calculus. This was also done for tanh-, bi-tanh- multiplicative, and bigeometric calculi and in the general case as well. Generalizations are also investigated where the homeomorphisms φ, η are arbitrary.