### Journals Information

Mathematics and Statistics Vol. 11(4), pp. 669 - 675
DOI: 10.13189/ms.2023.110408
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## Existence, Uniqueness, and Stability Results for Fractional Differential Equations with Lacunary Interpolation by the Spline Method

Ridha G. Karem 1, Karwan H. F. Jwamer 2,*, Faraidun K. Hamasalh 3
1 Department of Mathematics, College of Basic Education, University of Sulaimani, Iraq
2 Department of Mathematics, College of Science, University of Sulaimani, Iraq
3 Department of Mathematics, College of Education, University of Sulaimani, Iraq

ABSTRACT

Although there are theoretical conclusions about the existence, uniqueness, and properties of solutions to ordinary and partial differential equations, only the simplest and most straightforward particular problems can usually be solved explicitly, especially when nonlinear terms are involved, and we typically develop approximation. In order to resolve the form problem of fractional order beginning value (1) by lacunary interpolation with a fractional degree spline function, the main goal of this paper is to investigate and improve some approximate solutions as well as new approximate solution techniques that have been proposed for the first time. From a practical standpoint, the numerical solution of these differential equations is crucial because only a tiny portion of equations can be resolved analytically. For fractional differential equations that are sensitive to the beginning conditions, we provide a fractional spline approach. The polynomial coefficient-based spline interpolation must be constructed using the Caputo fractional integral and derivative. For the given spline function, a stability analysis is completed after investigating error boundaries. The numerical rationale for the suggested technique is thought to use three cases. The outcomes demonstrate how effective the spline fractional technique is in interpolating the coefficient with fractional polynomials. Finally, to demonstrate the effectiveness and correctness of the suggested strategy, general procedure programs are created in MATLAB and used to a number of instructive cases.

KEYWORDS
Stability Analysis, Fractional Polynomial, Fractional Derivative

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ridha G. Karem , Karwan H. F. Jwamer , Faraidun K. Hamasalh , "Existence, Uniqueness, and Stability Results for Fractional Differential Equations with Lacunary Interpolation by the Spline Method," Mathematics and Statistics, Vol. 11, No. 4, pp. 669 - 675, 2023. DOI: 10.13189/ms.2023.110408.

(b). APA Format:
Ridha G. Karem , Karwan H. F. Jwamer , Faraidun K. Hamasalh (2023). Existence, Uniqueness, and Stability Results for Fractional Differential Equations with Lacunary Interpolation by the Spline Method. Mathematics and Statistics, 11(4), 669 - 675. DOI: 10.13189/ms.2023.110408.