On the solution of \(\mathcal{T}-\)controllable abstract fractional differential equations with impulsive effects

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DOI:

https://doi.org/10.56754/0719-0646.2503.363

Abstract

In this research article, we delimitate the definition of mild solution for abstract fractional differential equations with state-dependent delay (AFDEw/SDD) of order \(\alpha\in(1,2)\) with impulsive effects and compare the solution to the second-order impulsive differential equations. Further, we obtain sufficient conditions of the existence of mild solution for instantaneous and non-instantaneous impulsive fractional functional differential inclusions with state-dependent delay (IFDIw/SDD) using the multi-valued fixed point theory and operator techniques. Furthermore, we study the trajectory controllability (\(\mathcal{T}-\)controllability) of the AFDEw/SDD. At last, we present some examples to illustrate the sufficient conditions involving partial and ordinary derivatives.

Keywords

Fractional differential equation , functional-differential equations with fractional derivatives , initial value problems , fixed point theorems , controllability

Mathematics Subject Classification:

34A08 , 34K37 , 34A12 , 37H10 , 93B05
  • Ganga Ram Gautam DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi-221005, India. https://orcid.org/0000-0002-2819-4076
  • Sandra Pinelas Department of Exact Sciences and Engineering, Academia Militar, Military Academy 2720-113 Amadora, Portugal. Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal. https://orcid.org/0000-0002-0984-0159
  • Manoj Kumar Department of mathematics, Deshbandhu College, University of Delhi, Delhi-110019, India.
  • Namrata Arya DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi-221005, India.
  • Jaimala Bishnoi Department of mathematics, Chaudhary Charan Singh University Meerut, Meerut-250001, India.
  • Pages: 363–386
  • Date Published: 2023-12-20
  • Vol. 25 No. 3 (2023)

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  • The Center for Research and Development in Mathematics and Applications
  • Portuguese Foundation for Science and Technology
  • UIDB/04106/2020
  • UIDP/04106/2020

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Published

2023-12-20

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G. Ram Gautam, S. Pinelas, M. Kumar, N. Arya, and J. Bishnoi, “On the solution of \(\mathcal{T}-\)controllable abstract fractional differential equations with impulsive effects”, CUBO, vol. 25, no. 3, pp. 363–386, Dec. 2023.

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