논문KCI 등재
Boundary Value Problems for differential Inclusions with Fractional Order
0
조회
0
다운로드
1
인용
0
참고문헌
키워드
주제분류수학
초록
In this paper, we shall establish sucient conditions for the existence of so-lutions for a class of boundary value problem for fractional dierential inclusionsinvolving the Caputo fractional derivative. The both cases of convex and non-convex valued right hand sides are considered.
Abstract
In this paper, we shall establish sucient conditions for the existence of so-lutions for a class of boundary value problem for fractional dierential inclusionsinvolving the Caputo fractional derivative. The both cases of convex and non-convex valued right hand sides are considered.
참고문헌 (40)
- R.P. Agarwal, "Boundary value problems for fractional differential equations", ~
- J.P. Aubin, "Differential Inclusions" (1984), Springer-Verlag
- J.P. Aubin, "Set-Valued Analysis" (1990), Birkhauser
- A. Belarbi, "Perturbed functional differential equations with fractional order", Commun. Appl. Anal, 11(3;4), pp.429~440 (2007)
- A. Belarbi, "Uniqueness results for fractional functional differential equations with infinite delay in Fr´echet spaces", Appl. Anal, 85, pp.1459~1470 (2006)
- M. Benchohra, "Existence results for fractional order functional differential equations with infinite delay", J. Math. Anal. Appl, 338(2), pp.1340~1350 (2008)
- C. Castaing, "Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics" (1977), Springer-Verlag
- H. Covitz, "Multivalued contraction mappings in generalized metric spaces", Israel J. Math, 8, pp.5~11 (1970)
- K. Deimling, "Multivalued Differential Equations" (1992), Walter De Gruyter
- D. Delbosco, "Existence and uniqueness for a nonlinear fractional differential equation", J. Math. Anal. Appl, 204, pp.609~625 (1996)
- K. Diethelm, "On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, in ”Scientifice Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties”", pp.217~224 (1999), Springer-Verlag
- K. Diethelm, "Analysis of fractional differential equations", J. Math. Anal. Appl, 265, pp.229~248 (2002)
- K. Diethelm, "Numerical solution of fractional order differential equations by extrapolation", Numer. Algorithms, 16, pp.231~253 (1997)
- A. Granas, "Fixed Point Theory" (2003), Springer-Verlag
- A.M.A. El-Sayed, "Fractional order evolution equations", J. Fract. Calc, 7, pp.89~100 (1995)
- A.M.A. El-Sayed, "Fractional order diffusion-wave equations", Intern. J. Theo. Physics, 35, pp.311~322 (1996)
- A.M.A. El-Sayed, "Nonlinear functional differential equations of arbitrary orders", Nonlinear Anal, 33, pp.181~186 (1998)
- A.M.A. El-Sayed, "Multivalued fractional differential equations", Appl. Math. Comput, 68, pp.15~25 (1995)
- L. Gaul, "Damping description involving fractional operators", Mech. Systems Signal Processing, 5, pp.81~88 (1991)
- W.G. Glockle, "A fractional calculus approach of selfsimilar protein dynamics", Biophys. J, 68, pp.46~53 (1995)
- Sh. Hu, "Handbook of Multivalued Analysis" (1997), Kluwer
- R. Hilfer, "Applications of Fractional Calculus in Physics" (2000), World Scientific
- M. Kisielewicz, "Differential Inclusions and Optimal Control" (1991), Kluwer
- A.A. Kilbas, "Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions", Differential Equations, 41, pp.84~89 (2005)
- A.A. Kilbas, "Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies" (2006), Elsevier Science B.V.
- V. Lakshmikantham, "Basic theory of fractional differential equations", Nonlinear Anal. Theory Methods (2007)
- V. Lakshmikantham, "Theory of fractional differential inequalities and applications", Commun. Appl. Anal, 11(3;4), pp.395~402 (2007)
- V. Lakshmikantham, "General uniqueness and monotone iterative technique for fractional differential equations", Appl. Math. Letters (2007)
- F. Mainardi, "Fractional calculus: Some basic problems in continuum and statistical mechanics, in ”Fractals and Fractional Calculus in Continuum Mechanics”", pp.291~348 (1997), Springer-Verlag
- F. Metzler, "Relaxation in filled polymers: A fractional calculus approach", J. Chem. Phys, 103, pp.7180~7186 (1995)
- K.S. Miller, "An Introduction to the Fractional Calculus and Differential Equations" (1993), John Wiley
- S.M. Momani, "Some comparison results for integro-fractional differential inequalities", J. Fract. Calc, 24, pp.37~44 (2003)
- S.M. Momani, "Some analytical properties of solutions of differential equations of noninteger order", Int. J. Math. Math. Sci, 2004, pp.697~701 (2004)
- K.B. Oldham, "The Fractional Calculus" (1974), Academic Press
- A. Ouahab, "Some results for fractional boundary value problem of differential inclusions", Nonlinear Anal (2007)
- I. Podlubny, "Fractional Differential Equations" (1999), Academic Press
- I. Podlubny, "Analogue realizations of fractional-order controllers. Fractional order calculus and its applications", Nonlinear Dynam, 29, pp.281~296 (2002)
- S.G. Samko, "Fractional Integrals and Derivatives. Theory and Applications" (1993), Gordon and Breach
- C. Yu, "Existence of fractional differential equations", J. Math. Anal. Appl, 310, pp.26~29 (2005)
- S. Zhang, "Positive solutions for boundary-value problems of nonlinear fractional diffrential equations", Electron. J. Diff. Equ, (36), pp.1~12 (2006)
관련 논문AI추천
Boundary value problems for differential equations of non-integer order involving Caputo fractional derivativeD.B.Dhaigude, J.A.Nanware장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제3호EXISTENCE RESULTS FOR FRACTIONAL DIFFERENTIAL INCLUSIONS WITH SEPARATED BOUNDARY CONDITIONSBashir Ahmad대한수학회 · 대한수학회보2010 · 제47권 제4호Existence results for boundary value problems for non-linear fractional integro differential inclusion with discrete delay and integral conditionsBRIJENDRA KUMAR CHAURASIYA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2025 · 제28권 제4호Nonlocal boundary value problems for Hilfer fractional differential equationsAtthapol Kijjathanakorn, Jessada Tariboon, Sotiris K. Ntouyas, Suphawat Asawasamrit대한수학회 · 대한수학회보2018 · 제55권 제6호On nonlinear fractional integro-differential equations with two boundary conditionsMACHINDRA B. DHAKNE, SABRI T. M. THABET장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호Fractional differential equations with nonlocal boundary conditionsAgus L. Soenjaya대한수학회 · 대한수학회논문집2022 · 제37권 제2호
이 간행물의 다른 논문 (12건)
A new note on power increasing sequencesHuseyin Borpp. 137-141Duality between the compact and discrete objects for noncommutative topological groupAlexander I. Shternpp. 143-154Modifications of an intuitionistic fuzzy implication from kleene-dienes typeLilja Atanassovapp. 155-160The modified q-Euler numbers and polynomialsTaekyun Kimpp. 161-170On some identities of Ramanujan found in his lost notebookD. Mamta, D.D. Somashekarapp. 171-180
