New attitude on sequential Ψ-Caputo differential equations via concept of measures of noncompactness

In this paper, we have explored the existence and uniqueness of solutions for a pair of nonlinear fractional integro-differential equations comprising of the Ψ-Caputo fractional derivative and the Ψ-Riemann–Liouville fractional integral. These equations are subject to nonlocal boundary conditions an...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2024; no. 1; pp. 116 - 19
Main Authors Agheli, Bahram, Darzi, Rahmat
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 05.09.2024
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Attitudes
Babenko’s attitude
Boundary conditions
Boundary value problems
Calculus
Condensing maps
Derivatives
Differential equations
Fractional calculus
Integrals
Mathematics
Mathematics and Statistics
Measure of noncompactness
Ψ-Caputo derivative
Measure of noncompactness
Condensing maps
Ψ-Caputo derivative
Babenko’s attitude
34B99
34A55
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Summary:In this paper, we have explored the existence and uniqueness of solutions for a pair of nonlinear fractional integro-differential equations comprising of the Ψ-Caputo fractional derivative and the Ψ-Riemann–Liouville fractional integral. These equations are subject to nonlocal boundary conditions and a variable coefficient. Our findings are drawn upon the Mittage–Leffler function, Babenko’s attitude, and topological degree theory for condensing maps and the Banach contraction principle. To further elucidate our principal outcomes, we have presented two illustrative examples.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03188-0