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Turkish Journal of Mathematics

DOI

10.3906/mat-1906-94

Abstract

In the most general case of $\omega$-weights, some normed functional spaces $% X_{\omega}^{p}(a,b)( 1\leq p\leq\infty)$, $AC_{\gamma,\omega}^n[a,b]$ and a generalization of the fractional integro-differentiation operator are introduced and analyzed. The boundedness of the $\omega$-weighted fractional operator over $X_{\omega}^{p}(a,b)$ is proved. Some theorems and lemmas on the properties of the invertions of the mentioned operator and several representations of functions from $AC_{\gamma,\omega}^n[a,b]$ are established. A general $\omega$-weighted Caputo fractional derivative of order $\alpha$ is studied over $AC_{\gamma,\omega}^n[a,b]$. Some representations and other properties of this fractional derivative are proved. Some conclusions are presented.

First Page

662

Last Page

675

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Mathematics Commons

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