EXISTENCE OF WEAK SOLUTIONS FOR <i>Ψ</i>-CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEM VIA VARIATIONAL METHODS

Adnan Khaliq; Mujeeb ur Rehman

doi:10.11948/20200115

2021 Volume 11 Issue 4

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Adnan Khaliq, Mujeeb ur Rehman. EXISTENCE OF WEAK SOLUTIONS FOR Ψ-CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEM VIA VARIATIONAL METHODS[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1768-1778. doi: 10.11948/20200115

Citation:

Adnan Khaliq, Mujeeb ur Rehman. EXISTENCE OF WEAK SOLUTIONS FOR Ψ-CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEM VIA VARIATIONAL METHODS[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1768-1778. doi: 10.11948/20200115

EXISTENCE OF WEAK SOLUTIONS FOR Ψ-CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEM VIA VARIATIONAL METHODS

Adnan Khaliq^1, ,,
Mujeeb ur Rehman¹

1.
Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan

Corresponding author: Email address: adnankhaliqsns@gmail.com (Adnan Khaliq)

Abstract

Abstract

This article is about a ψ-Caputo fractional boundary value problem which is investigated with the help of variational methods and critical point theory. A touchstone is obtained on the existence of the solution of the problem with the help of a functional. The problem is reduced into an equivalent form such that the solutions of the problem coincide with the critical points of a functional. Using aid from critical point theory, sufficient conditions are obtained for the existence of at least one solution. In the end, an example is also given to enrich our results.
- ψ-Caputo fractional differential operator /
- weak solution /
- critical point theory
MSC: 26A33, 34A08, 46E15, 58K05

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References

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