RESULT ON CONTROLLABILITY OF HILFER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS OF SOBOLEV-TYPE WITH NON-INSTANTANEOUS IMPULSE

Parveen Kumar, Ramesh Kumar Vats, Ankit Kumar

Abstract


This paper is concerned with the Hilfer fractional differential equations (HFDEs) of Sobolev-type with impulses that are not instantaneous in a Banach space. The presented work is based on the theory of propagation family {P(τ)}τ≥0, (generated by the operator pair (A , R)), measure of non-compactness (MNC), the fixed point methods. The primary goal of this study is to determine the controllability of a dynamical system without assuming that R-1 is a bounded operator, and that there is no any relationship between the domain of A and R. In addition, we provide a concrete application to support our main finding.

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