Upper and lower solutions for an integral boundary problem with two different orders (p,q)-fractional difference

In this paper, a ( p , q ) -fractional nonlinear difference equation of different orders is considered and discussed. With the help of ( p , q ) -calculus for integrals and derivatives properties, we convert the main integral boundary value problem (IBVP) to an equivalent solution in the form of an...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2024; no. 1; p. 104
Main Authors Mesmouli, Mouataz Billah, Al-Askar, Farah M., Mohammed, Wael W.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2024
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Boundary value problems
Calculus
Difference equations
Integral equations
Mathematics
Mathematics and Statistics
IBVP
difference fractional derivatives
47H10
Positive solutions
34A12
Fixed point
34A08
34B18
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Summary:In this paper, a ( p , q ) -fractional nonlinear difference equation of different orders is considered and discussed. With the help of ( p , q ) -calculus for integrals and derivatives properties, we convert the main integral boundary value problem (IBVP) to an equivalent solution in the form of an integral equation, we use the upper–lower solution technique to prove the existence of positive solutions. We present an example of the IBVP to apply and demonstrate the results of our method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1025-5834
1029-242X
DOI:10.1186/s13660-024-03185-3