EXISTENCE RESULTS FOR A NONLINEAR GENERALIZED CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEM

Serap Yalçın; Erbil Çetin; Fatma Serap Topal

doi:10.11948/20230359

2024 Volume 14 Issue 6

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Serap Yalçın, Erbil Çetin, Fatma Serap Topal. EXISTENCE RESULTS FOR A NONLINEAR GENERALIZED CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEM[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3639-3656. doi: 10.11948/20230359

Citation:

Serap Yalçın, Erbil Çetin, Fatma Serap Topal. EXISTENCE RESULTS FOR A NONLINEAR GENERALIZED CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEM[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3639-3656. doi: 10.11948/20230359

EXISTENCE RESULTS FOR A NONLINEAR GENERALIZED CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEM

1.
Department of Mathematics, Ege University, Bornova, 35100, Izmir, Turkey

Author Bio: Email: serapyallcin@gmail.com(S. Yalçın); Email: f.serap.topal@ege.edu.tr(F. S. Topal)
Corresponding author: Email: erbil.cetin@ege.edu.tr(E. Çetin)

Abstract

Abstract

This study gives some new existence results for a three point boundary value problem involving a nonlinear fractional differential equation that incorporates a broad form of the Caputo fractional derivative concerning a new function. Our approach rests upon the fixed point theorems established by Banach, Schafer, and Schauder. Additionally, we substantiate the robustness of our findings by providing an apt illustrative example.
- Fractional differential equation /
- Caputo fractional derivative /
- generalized Caputo fractional derivative and fractional integral /
- existence result /
- fixed point theorem /
- upper and lower solution
MSC: 26A33, 34K10, 34K37

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References

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