SOME NEW EXISTENCE RESULTS FOR BOUNDARY VALUE PROBLEMS INVOLVING [psi]-CAPUTO FRACTIONAL DERIVATIVE

This paper concerns the boundary value problem for a fractional differential equation involving a generalized Caputo fractional derivative in b-metric spaces. The used fractional operator is given by the kernel k(t,s) = [psi](t) - [psi](s) and the derivative operator 1/[psi]'(t) d/dt. Some exis...

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Published inTWMS journal of applied and engineering mathematics Vol. 13; no. 1; p. 246
Main Authors Afshari, H, Abdo, M. S, Sahlan, M. N
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2023
Elman Hasanoglu
Subjects
Boundary value problems
Fixed point theory
Fixed points (mathematics)
Mathematical research
Mathematics
Operators (mathematics)
Iran
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Summary:This paper concerns the boundary value problem for a fractional differential equation involving a generalized Caputo fractional derivative in b-metric spaces. The used fractional operator is given by the kernel k(t,s) = [psi](t) - [psi](s) and the derivative operator 1/[psi]'(t) d/dt. Some existence results are obtained based on fixed point theorem of [alpha]-[phi]--Graghty contraction type mapping. In the end, we provide some illustrative examples to justify the acquired results. Keywords: [psi]--Caputo fractional derivative, Boundary value problem (BVP), [alpha]-[phi]--Geraghty contractive type mapping, Fixed point (FP). AMS Subject Classification: 83-02, 99A00.
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ISSN:2146-1147
2146-1147