ON BEST PROXIMITY POINT APPROACH TO SOLVABILITY OF A SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS

Pradip Ramesh Patle; Moosa Gabeleh; Manuel De La Sen

doi:10.11948/20230007

2023 Volume 13 Issue 6

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Pradip Ramesh Patle, Moosa Gabeleh, Manuel De La Sen. ON BEST PROXIMITY POINT APPROACH TO SOLVABILITY OF A SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3294-3307. doi: 10.11948/20230007

Citation:

Pradip Ramesh Patle, Moosa Gabeleh, Manuel De La Sen. ON BEST PROXIMITY POINT APPROACH TO SOLVABILITY OF A SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3294-3307. doi: 10.11948/20230007

ON BEST PROXIMITY POINT APPROACH TO SOLVABILITY OF A SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS

1.
Department of Mathematics, School of Advanced Sciences, VIT-AP University, 522237 Amravati, India
2.
Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
3.
Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Bizkaia, Spain

Author Bio: Email: pradip.patle12@gmail.com(P. R. Patle); Email: manuel.delasen@ehu.eus(M. De La Sen)
Corresponding author: Email: gabeleh@abru.ac.ir, gab.moo@gmail.com(M. Gebeleh)

Abstract

Abstract

In this article, a class of cyclic (noncyclic) condensing operators is defined on a Banach space using the notion of measure of noncompactness and $ C $-class functions. For these newly defined condensing operators, best proximity point (pair) results are manifested. Then the obtained main results are applied to demonstrate the existence of optimum solutions of a system of fractional differential equations involving $ \psi $-Hilfer fractional derivatives.
- Best proximity point (pair) /
- measure of noncompactness /
- Hilfer fractional differential equation /
- $\psi$-Hilfer fractional derivative /
- cyclic mapping /
- noncyclic mapping
MSC: 47H10, 34A08, 47H08, 47H09

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References

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