Existence, uniqueness and approximation of nonlocal fractional differential equation of sobolev type with impulses-Reference-Cited by-同舟云学术

Existence, uniqueness and approximation of nonlocal fractional differential equation of sobolev type with impulses

Published:2023 Issue:2 Volume:8 Page:4645-4665
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Manjula M.¹,Kaliraj K.¹,Botmart Thongchai²,Nisar Kottakkaran Sooppy³,Ravichandran C.⁴

Affiliation:

1. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, Tamil Nadu, India

2. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

3. Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia

4. Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029, Tamil Nadu, India

Abstract

<abstract><p>This paper is concerned with the study of nonlocal fractional differential equation of sobolev type with impulsive conditions. An associated integral equation is obtained and then considered a sequence of approximate integral equations. By utilizing the techniques of Banach fixed point approach and analytic semigroup, we obtain the existence and uniqueness of mild solutions to every approximate solution. Then, Faedo-Galerkin approximation is used to establish certain convergence outcome for approximate solutions. In order to illustrate the abstract results, we present an application as a conclusion.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference39 articles.

1. K. Kavitha, V. Vijayakumar, R. Udhayakumar, Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness, Chaos Solitons Fractals, 139 (2020), 110035. https://doi.org/10.1016/j.chaos.2020.110035

2. H. M. Ahmed, H. M. El-Owaidy, M. A. AL-Nahhas, Neutral fractional stochastic partial differential equations with Clarke subdifferential, Appl. Anal., 100 (2021), 3220–3232. https://doi.org/10.1080/00036811.2020.1714035

3. K. S. Nisar, K. Jothimani, K. Kaliraj, C. Ravichandran, An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain, Chaos Solitons Fractals, 146 (2021), 110915. https://doi.org/10.1016/j.chaos.2021.110915

4. K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, New York: Wiley, 1993.

5. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, In: North-holland mathematics studies, Amsterdam: Elsevier, 204 (2006), 1–523.

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