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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 1

Nonlocal boundary value problems for nonlineartoppled system of fractional differential equations

Kamal SHAH
Sayfa
316–337
Yayın Tarihi
2022-10-18
DOI
—
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The results are demonstrated by providingseveral examples.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The aim of this paper is to study multiplicity results for the solutions of a coupled system offractional differential equations.
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Temel Bulgular & Veri:The problem under consideration is subjected to nonlocalboundary conditions involving Riemann-Liouville integrals and derivatives of fractionalorder.
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Sonuç & Katkı:The results are demonstrated by providingseveral examples.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

The aim of this paper is to study multiplicity results for the solutions of a coupled system offractional differential equations. The problem under consideration is subjected to nonlocalboundary conditions involving Riemann-Liouville integrals and derivatives of fractionalorder. Necessary and sufficient conditions are established for the existence of at leastone and more solutions by using various fixed point theorems of cone type. Moreoversufficient conditions for uniqueness is also discussed by using a concave type operatorfor the considered problem. Further, the conditions are also provided under which theconsidered system has no positive solution. The results are demonstrated by providingseveral examples.

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Bu Makaleye Atıf Yap

SHAH, K. (2022). Nonlocal boundary value problems for nonlineartoppled system of fractional differential equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 316–337. https://ajindex.com/articles/530058

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  1. Y. Cui, and Y. Zou,Existence results and the monotone iterative technique for nonlin-ear fractional differential systems with coupled four-point Boundary Value Problems,Abst. Appl. Anal., Art. ID 242591, 6 pp, 2014. [2]K. Deimling,Nonlinear functional analysis, Springer-Verlag, New York, 1985. [3]R. Hilfer,Applications of Fractional Calculus in Physics, World Scientific, Singapore,2000. [4]X. Han and T. Wang,The existence of solutions for a nonlinear fractional multi-point boundary value problem at resonance, Int. J. Differ. Equ. Art., ID 401803, 14pp., 2011. [5]M. Jleli and B. Samet,Existence of positive solutions to a coupled system of fractionaldifferential equation, Math. Methods Appl. Sci.38(6), 1014-1031, 2015. [6]R.A.Khan and K.Shah,Existence and uniqueness of solutions to fractional ordermulti-point boundary value problems, Commun. Appl. Anal.19, 515−526, 2015. [7]R.A. Khan,Existence and approximation of solutions to three-point boundary valueproblems for fractional differential equations, Electron. J. Qual. Theory Differ. Equ.58, 25−35, 2011. [8]R.A. Khan and M. Rehman,Existence of multiple positive solutions for a generalsystem of fractional differential equations, Commun. Appl. Nonlinear Anal.18, (2011)25−35. [9]A.A. Kilbas, H. Srivastava and J. Trujillo,Theory and application of fractional differ-ential equations, North Holland Mathematics Studies, vol. 204, Elseveir, Amsterdam,2006. [10]R.W. Leggett and L.R Williams,Multiple positive fixed points of nonlinear operatorson ordered Banach spaces, Indiana Univ. Math. J.28, 673−688, 1979. [11]Y. Liu,Solvability of multi-point boundary value problems for multiple term Riemann-Liouville fractional differential equations, Comput. Math. Appl.64, 413−431, 2012. [12]R. Ma,A survey On nonlocal boundary value problems,Applied Mathematics E-Notes.7, 257−279, 2007. [13]K.S. Miller and B. Ross,An Introduction to the Fractional Calculus and FractionalDifferential Equations,Wiley, New York, 1993. [14]K.S. Miller and B. Ross,An Introduction to the Fractional Calculus and FractionalDifferential Equations, Wiley, New York, 1993. [15]I. Podlubny,Fractional differential equations, Academic press, New York, 1993. [16]P.H. Rabinowitz,A note on a nonlinear eigenvalue problem for a class of differentialequations, J. Differential Equations9, 536−548, 1971. [17]B.P. Rynne,Spectral properties and nodal solutions for second-order, m-point, bound-ary value problems, Nonlinear Anal.67(12), 3318−3327, 2007. [18]J. Sabatier,