Analysis of fractional global differential equations with power law

Abdon Atangana; Muhammad Altaf Khan; Abdon Atangana; Muhammad Altaf Khan

doi:10.3934/math.20231259

AIMS Mathematics

2023, Volume 8, Issue 10: 24699-24725. doi: 10.3934/math.20231259

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Research article

Analysis of fractional global differential equations with power law

Abdon Atangana ^1,2,
Muhammad Altaf Khan ^{1
,
,}

1.
Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 26 June 2023 Revised: 02 August 2023 Accepted: 07 August 2023 Published: 21 August 2023
MSC : 26A33, 34A08

We have considered a special class of ordinary differential equations in which the differential operators are those of the Caputo fractional global derivative. These equations are generalizations of the well-known differential equations with the Caputo fractional derivative. Due to the various possible applications of these equations to model real-world problems we have first introduced some new inequalities that will be used in all fields of science, technology and engineering where these equations could be applied. We used Nagumo's principles to establish the existence and uniqueness of the solution for this class of equations with additional conditions. We have applied the midpoint principle to obtain a numerical scheme that will be used to solve these equations numerically. Some illustrative examples are presented with excellent results.
- numerical scheme,
- power law kernel,
- global derivative,
- Nagumo's principles
Citation: Abdon Atangana, Muhammad Altaf Khan. Analysis of fractional global differential equations with power law[J]. AIMS Mathematics, 2023, 8(10): 24699-24725. doi: 10.3934/math.20231259

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Abstract

We have considered a special class of ordinary differential equations in which the differential operators are those of the Caputo fractional global derivative. These equations are generalizations of the well-known differential equations with the Caputo fractional derivative. Due to the various possible applications of these equations to model real-world problems we have first introduced some new inequalities that will be used in all fields of science, technology and engineering where these equations could be applied. We used Nagumo's principles to establish the existence and uniqueness of the solution for this class of equations with additional conditions. We have applied the midpoint principle to obtain a numerical scheme that will be used to solve these equations numerically. Some illustrative examples are presented with excellent results.

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