Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with $\mho$-Caputo Fractional Differential Equations

Abduljawad Anwar

doi:10.33434/cams.1556314

EN

Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with $\mho$-Caputo Fractional Differential Equations

Abstract

This paper examines the existence, uniqueness, and Ulam-Hyers stability of solutions to nonlinear $\mho$-fractional differential equations with boundary conditions with a $\mho$-Caputo fractional derivative. The acquired results for the suggested problem are validated using a novel technique and minimum assumptions about the function $f$. The analysis reduces the problem to a similar integral equation and uses Banach and Sadovskii fixed point theorems to reach the desired findings. Finally, the inquiry is demonstrated by illustrative example to validate the theoretical findings.

Keywords

Banach Contraction mapping, Caputo fractional derivative, $\mho$-Caputo fractional derivative, Fixed point theorem, Fractional differential equations, Stability analysis, Ulam-Hyers stability

References

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Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems, Pure Mathematics (Other)

Journal Section

Research Article

Authors

Abduljawad Anwar ^*
0009-0007-0864-4870
Iraq

Early Pub Date

December 12, 2024

Publication Date

December 31, 2024

Submission Date

September 26, 2024

Acceptance Date

November 27, 2024

Published in Issue

Year 2024 Volume: 7 Number: 4

DOI

https://doi.org/10.33434/cams.1556314

IZ

https://izlik.org/JA44BU67JC

APA

Anwar, A. (2024). Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with $\mho$-Caputo Fractional Differential Equations. Communications in Advanced Mathematical Sciences, 7(4), 187-198. https://doi.org/10.33434/cams.1556314

AMA

1.Anwar A. Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with $\mho$-Caputo Fractional Differential Equations. Communications in Advanced Mathematical Sciences. 2024;7(4):187-198. doi:10.33434/cams.1556314

Chicago

Anwar, Abduljawad. 2024. “Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations With $\mho$-Caputo Fractional Differential Equations”. Communications in Advanced Mathematical Sciences 7 (4): 187-98. https://doi.org/10.33434/cams.1556314.

EndNote

Anwar A (December 1, 2024) Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with $\mho$-Caputo Fractional Differential Equations. Communications in Advanced Mathematical Sciences 7 4 187–198.

IEEE

[1]A. Anwar, “Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with $\mho$-Caputo Fractional Differential Equations”, Communications in Advanced Mathematical Sciences, vol. 7, no. 4, pp. 187–198, Dec. 2024, doi: 10.33434/cams.1556314.

ISNAD

Anwar, Abduljawad. “Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations With $\mho$-Caputo Fractional Differential Equations”. Communications in Advanced Mathematical Sciences 7/4 (December 1, 2024): 187-198. https://doi.org/10.33434/cams.1556314.

JAMA

1.Anwar A. Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with $\mho$-Caputo Fractional Differential Equations. Communications in Advanced Mathematical Sciences. 2024;7:187–198.

MLA

Anwar, Abduljawad. “Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations With $\mho$-Caputo Fractional Differential Equations”. Communications in Advanced Mathematical Sciences, vol. 7, no. 4, Dec. 2024, pp. 187-98, doi:10.33434/cams.1556314.

Vancouver

1.Abduljawad Anwar. Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with $\mho$-Caputo Fractional Differential Equations. Communications in Advanced Mathematical Sciences. 2024 Dec. 1;7(4):187-98. doi:10.33434/cams.1556314

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https://doi.org/10.52280/pujm.2024.56(10)04

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