Analysis and some applications of a regularized Ψ–Hilfer fractional derivative

The main purpose of this research is to present a generalization of Ψ–Hilfer fractional derivative, called as regularized Ψ–Hilfer, and study some of its basic characteristics. In this direction, we show that the ψ–Riemann–Liouville integral is the inverse operation of the presented regularized diff...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 415; p. 114476
Main Authors: Jajarmi, Amin, Baleanu, Dumitru, Sajjadi, Samaneh Sadat, Nieto, Juan J.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2022
Subjects:
Existence and uniqueness
Fractional derivative
Numerical method
Regularized [formula omitted]–Hilfer
Numerical method
Regularized ψ–Hilfer
Existence and uniqueness
Fractional derivative
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:The main purpose of this research is to present a generalization of Ψ–Hilfer fractional derivative, called as regularized Ψ–Hilfer, and study some of its basic characteristics. In this direction, we show that the ψ–Riemann–Liouville integral is the inverse operation of the presented regularized differentiation by means of the same function ψ. In addition, we consider an initial-value problem comprising this generalization and analyze the existence as well as the uniqueness of its solution. To do so, we first present an approximation sequence via a successive substitution approach; then we prove that this sequence converges uniformly to the unique solution of the regularized Ψ–Hilfer fractional differential equation (FDE). To solve this FDE, we suggest an efficient numerical scheme and show its accuracy and efficacy via some real-world applications. Simulation results verify the theoretical consequences and show that the regularized Ψ–Hilfer fractional mathematical system provides a more accurate model than the other kinds of integer- and fractional-order differential equations.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114476