Bifurcation from interval and multiple positive solutions for a nonlinear fractional differential equations with integral boundary conditions

Authors

  • Madjid Halaoua
  • El Amir Djeffal

DOI:

https://doi.org/10.54019/sesv4n1-017

Keywords:

positive solution, fractional differential equation, integral boundary condition, bifurcation technique

Abstract

This paper studies the bifurcation from interval and Multiple positive solutions for a boundary-value problem of nonlinear fractional differential equations with integral boundary conditions. Using the bifurcation technique and the topological degree theory, the existence of Multiple positive solutions is investigated and some sufficient conditions are obtained.

References

J. T. A.A. Kilbas, H.M. Srivastava. Theory and Applications of Fractional Differential Equations. North-Holland Math. Stud., vol. 204, Elsevier Science B.V., Amsterdam, 2006.

A. Cabada and G. Wang. Positive solutions of nonlinear fractional differential equations with integral boundary value conditions. J.Math. Anal.Appl., 389:403–411, (2012).

Y. L. C.C. Tian. Multiple positive solutions for a class of fractional singular boundary value problems. Mem. Differ. Equ. Math. Phys, 56:115—-131, (2012).

Z. X. G. W. Feng, M. New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions. Bound. Value Probl, vol 2011:Article ID 720702, (2011).

D. Guo. Nonlinear Functional Analysis. Shandong Science and Technology Press, Jinan, 2001.

D. Jiang and C. Yuan. The positive properties of the green function for dirichlet-type boundary value problems of nonlinearfractional differential equations and its application. Nonlinear Analysis, Theory, Methods Applications, vol. 72, no. 2,pp:710—-719, (2010).

P. Li and Z. Yong. Bifurcation from interval and positive solutions of the three-point boundary value problem for fractional differential equations. Applied Mathematics and Computation, 257:458––466, (2015).

Y. Liu. Positive solutions using bifurcation techniques for boundary value problems of fractional differential equations. Abstract and Applied Analysis, vol 2013:Article ID 162418, 7 pages, (2013).

Y. Liu and H. Yu. Bifurcation of positive solutions for a class of boundary value problems of fractional differential inclusions. J. Diff. Equat., vol 2013:Article ID 942831, 8 pages, (2013).

A. S. c. M.P. Lazarevi c. Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach. Math. Comput. Modelling, 49:475—-481, (2009).

I. Podlubny. Fractional Differential Equations. Math. Sci. Eng., Academic Press, New York, 1999.

P. Rabinowitz. Some global results for nonlinear eigenvalue problems. J. Funct. Anal., 7:487–513, (1971).

P. Rabinowitz. On bifurcation from infinity. J. Diff. Equat., 14:462–475, (1973).

H. Salem. Fractional order boundary value problem with integral boundary conditions involving pettis integral. Acta Math. Sci., Ser. B, Engl. Ed, vol 31 (2):661–672, (2011).

K. Schmitt. Positive solutions of semilinear elliptic boundary value problems. In Topological Methods in Differential Equations and Inclusions, vol. 472, pp. 447–500, Kluwer Academic Publishers, Dordrecht,The Netherlands, 1995.

K. Schmitt and R. C. Thompson. Nonlinear Analysis and Differential Equations: An Introduction. University of Utah Lecture Note, Salt Lake City, Utah, USA, 2004.

Z. M. Sun, Y. Positive solutions for a class of fractional differential equations with integral boundary conditions. Appl. Math. Lett., 34:17–21, (2012).

A. V. V. Lakshmikantham. Basic theory of fractional differential equations. Nonlinear Anal., 69:2677—-2682, (2008).

A. V. V. Lakshmikantham. Basic theory of fractional differential equations. Nonlinear Anal., 69:2677––2682, (2008).

J. C. W.Z. Li, Q.D. Li. Initial value problems for fractional differential equations involving riemann–liouville sequential fractional derivative. J. Math. Anal. Appl., 367 (1):260––272, (2010).

F. J. Y. Zhou. Nonlocal cauchy problem for fractional evolution equations. Nonlinear Anal. Real World Appl, 11:4465–4475, (2010).

L. Yansheng. Bifurcation techniques for a class of boundary value problems of fractional impulsive differential equations. Journal of nonlinear Science and Applications, 8:340–353, (2015).

T. Q. Z.B. Bai. Existence of positive solution for singular fractional differential equation. Appl. Math. Comput, 215 (7):2761—-2767, (2009).

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Published

2023-12-28

How to Cite

Halaoua, M., & Djeffal, E. A. (2023). Bifurcation from interval and multiple positive solutions for a nonlinear fractional differential equations with integral boundary conditions. STUDIES IN EDUCATION SCIENCES, 4(1), 243–265. https://doi.org/10.54019/sesv4n1-017