Composition and convolution theorems for μ-Stepanov pseudo almost periodic functions and applications to fractional integro-differential equations
| dc.contributor.author | Alvarez, Edgardo | |
| dc.date.accessioned | 2022-01-03T16:22:35Z | |
| dc.date.available | 2022-01-03T16:22:35Z | |
| dc.date.issued | 2018-01-18 | |
| dc.description.abstract | In this article we establish new convulsion and composition theorems for μ-Stepanov pseudo almost periodic functions. We prove that the space of vector-valued μ-Stepanov pseudo almost periodic functions is a Banach space. As an application, we prove the existence and uniqueness of μ-pseudo almost periodic mild solutions for the fractional integro-differential equation. Dαu(t) = Au(t) + ∫t-∞ α(t - s) Au(s) ds + ƒ(t, u(t)), where A generates an α-resolvent family {Sα(t)}t ≥ 0 on a Banach space X, α ∈ L1loc (ℝ+), α > 0, the fractional derivative is understood in the sense of Weyl and the nonlinearity ƒ is a μ-Stepanov pseudo almost periodic function. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 15 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Alvarez, E. (2018). Composition and convolution theorems for μ-Stepanov pseudo almost periodic functions and applications to fractional integro-differential equations. <i>Electronic Journal of Differential Equations, 2018</i>(27), pp. 1-15. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15083 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | μ-Stepanov pseudo almost periodic | |
| dc.subject | Mild solutions | |
| dc.subject | Fractional integro-differential equations | |
| dc.subject | Composition | |
| dc.subject | Convolution | |
| dc.title | Composition and convolution theorems for μ-Stepanov pseudo almost periodic functions and applications to fractional integro-differential equations | |
| dc.type | Article |