Study of fractional evolution equations involving Hilfer fractional derivative of order $1<γ<2$ and type $0 \leq δ\leq 1$

Anjali Jaiswal; D. Bahuguna

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arXiv · 1907.11470

Study of fractional evolution equations involving Hilfer fractional derivative of order $1<γ<2$ and type $0 \leq δ\leq 1$

Anjali Jaiswal·D. Bahuguna

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Abstract

In this paper we investigate fractional differential equations with Hilfer fractional derivative of order $1<γ<2$ and type $δ\in [0,1]$ in a Banach space. We introduce a family of general fractional cosine operator functions of order $1<γ<2$ and type $δ\in [0,1]$ and discuss their properties to give a suitable definition of mild solution of a semilinear evolution equation. In last section an example is presented.

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Anjali Jaiswal, D. Bahuguna. 2020-12-04. Study of fractional evolution equations involving Hilfer fractional derivative of order $1<γ<2$ and type $0 \leq δ\leq 1$. https://arxiv.org/abs/1907.11470

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