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International Conference on Differential & Difference Equations and Applications

ICDDEA 2015: Differential and Difference Equations with Applications pp 25–37Cite as

Existence of the Mild Solutions for Nonlocal Fractional Differential Equations of Sobolev Type with Iterated Deviating Arguments

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 164))

Abstract

This paper investigates a nonlocal differential equation of Sobolev type of fractional order with iterated deviating arguments in Banach space. The sufficient condition for providing the existence of mild solution to the nonlocal Sobolev-type fractional differential equation with iterated deviating arguments is obtained via technique of fixed-point theorems and analytic semigroup method. Finally, an example is given to explain the applicability of the abstract results developed.

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Acknowledgements

The authors would like to thank the referee for important remarks and suggestions. The work of the first author is supported by the Indian Institute of Technology, Roorkee, IIT Roorkee Heritage, CSIR, New Delhi, with Ref number-TG∕8753∕14 − HRD and the University Grants Commission (UGC), Government of India, New Delhi, under grant number 6405-11-61.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Alka Chadha & Dwijendra N. Pandey

Authors
  1. Alka Chadha
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  2. Dwijendra N. Pandey
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Correspondence to Alka Chadha .

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Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Zuzana Došlá

  3. Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Ondřej Došlý

  4. School of Mathematics and Stastistics, Huazhong University of Science and Technology, Wuhan, China

    Peter E. Kloeden

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Chadha, A., Pandey, D.N. (2016). Existence of the Mild Solutions for Nonlocal Fractional Differential Equations of Sobolev Type with Iterated Deviating Arguments. In: Pinelas, S., Došlá, Z., Došlý, O., Kloeden, P. (eds) Differential and Difference Equations with Applications. ICDDEA 2015. Springer Proceedings in Mathematics & Statistics, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-319-32857-7_3

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