On the Caputo-Hadamard fractional IVP with variable order using the upper-lower solutions technique-Reference-Cited by-同舟云学术

On the Caputo-Hadamard fractional IVP with variable order using the upper-lower solutions technique

Published:2022 Issue:3 Volume:8 Page:5484-5501
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Bouazza Zoubida¹,Souhila Sabit²,Etemad Sina³,Souid Mohammed Said⁴,Akgül Ali⁵⁶,Rezapour Shahram³⁷,De la Sen Manuel⁸

Affiliation:

1. Department of Informatics, University of Tiaret, Tiaret, Algeria

2. Laboratoire Matériaux et Structures, Departement of Mathematics, University of Tiaret, Tiaret, Algeria

3. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

4. Department of Economic Sciences, University of Tiaret, Tiaret, Algeria

5. Department of Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, Türkiye

6. Mathematics Research Center, Department of Mathematics, Near East University, North Cyprus, Mersin 10, Nicosia 99138, Türkiye

7. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

8. Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, Leioa 48940, Bizkaia, Spain

Abstract

<abstract><p>This paper studies the existence of solutions for Caputo-Hadamard fractional nonlinear differential equations of variable order (CHFDEVO). We obtain some needed conditions for this purpose by providing an auxiliary constant order system of the given CHFDEVO. In other words, with the help of piece-wise constant order functions on some continuous subintervals of a partition, we convert the main variable order initial value problem (IVP) to a constant order IVP of the Caputo-Hadamard differential equations. By calculating and obtaining equivalent solutions in the form of a Hadamard integral equation, our results are established with the help of the upper-lower-solutions method. Finally, a numerical example is presented to express the validity of our results.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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