Generalized Complex Conformable Derivative and Integral Bases in Fréchet Spaces

Abstract

This paper presents an additional approach in the field of polynomial bases, utilizing generalized complex conformable fractional derivative and integral operators. These operators are applied to polynomial bases of complex conformable derivatives (GCCDB) and generalized complex conformable integrals (GCCIB) in Fréchet spaces . We also investigate their convergence properties within closed disks , open disks, open regions surrounding closed disks , origin and for all entire functions , employing the Cannon sum , order, type and T_ρ-property as convergence criteria for our study. The significance of this work lies in generalizing certain previous studies and considering them as special cases of it. Additionally , this paper concludes examples and applications that illustrate the concepts of Generalized Complex Conformable derivative base of polynomials and Generalized Complex conformable integral of polynomials in Fréchet spaces . 2000 Mathematics Subject Classification: 30G35, 41A10.Keywords Conformable derivative, Conformable integral, basic set, order, type, T_ρ-property.