### Positive solutions for fractional differential equations with non-separated type nonlocal multi-point and multi-term integral boundary conditions

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Agarwal, R. P., Alsaedi, A., Alsharif, A., Ahmad, B., On nonlinear fractional-order boundary value problems with nonlocal multi-point conditions involving Liouville-Caputo derivatives, Differ. Equ. Appl., Volume 9, Number {bf{2}} (2017), 147--160, doi:10.7153/dea-09-12.

Bouteraa, N., Benaicha, S., Djourdem, H., Positive solutions for anonlinear fractional differential equation with nonlocal boundary conditions, Universal Journal of Mathematics and Applications., 1 {bf(1)} (2018), 39--45.

Bouteraa, N., Benaicha, S., Existence of solutions for three-point boundary value problem for nonlinear fractional differential equations, Bulletin of the Transilvania University of Brasov, Series III: Mathematics, Informatics, Physics., Vol 10(59), No. 1 – 2017.

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

Cui, Y., Zou, Y., Existence of solutions for second-order integral boundary value problems. Nonlinear Anal., Model. Control., {bf{21}}(2016), 828–-838.

Delbosco, D., Fractional calculus and function spaces, J. Fract. Calc., {bf{6}} (1996), 45–-53.

Diethelm, l., Freed, K.,: On the solutions of nonlinear fractional order differential equations used in the modelling of viscoplasticity. In: Keil, F, Mackens, W, Voss, H, Werthers, J (eds.) Scientific Computing in Chemical Engineering II - Computational Fluid Dynamics, Reaction Engineering and Molecular Properties. Springer, Heidelberg., (1999).

Djourdem, H., S. Benaicha, S., Existence of positive solutions for a nonlinear three-point boundary value problem with integral boundary conditions. Acta Math. Univ. Comenianae., Vol 87, {bf{2}} (2018) pp 167--177.

Glockle, WG., Nonnenmacher, TF., A fractional calculus approach of self-similar protein dynamics. Biophys. J., {bf{68}}(1995), 46--53.

Guo, D., V. Lakshmikantham, V., Nonlinear Problems in Abstract Cones. Academic Press, New York., (1988).

Guo, L., Liu, L., Wu, Y., Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions.Nonlinear Analysis: Modelling and Control., Vol. 21, No. {bf{5}} 2016, 635–-650.

He, J., Some applications of nonlinear fractional differential equations and their approximations. Bull. Am. Soc. Inf. Sci. Technol., {bf{15}}(1999), 86–-90 .

Henderson, J., Luca, R., Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems. Nonlinear Differ. Equ. Appl., {bf{20}} (2013), 1035–-1054

Henderson, J., Luca, R., Systems of Riemann–Liouville fractional equations with multi-point boundary conditions. Appl. Math. Comput., {bf{309}} (2017), 303-–323.

Henderson, J., Luca, R., Tudorache, A., On a system of fractionl differential equations with coupled integral boundary conditions. Fract. Calc. Appl. Anal., {bf{18}}(2015), 361--386.

Kilbas, AA., Srivastava, HM., Trujillo, JJ., Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, 2006.

Leggett, R.W., Williams, L.R., Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana Univ. Math. J., {bf{28}} (1979), 673--688.

Liu, L., Jiang, J., Wu, Y., The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems. J. Nonlinear Sci. Appl., 9{bf{(5)}} (2016), 2943–-2958.

Ma, D-X., Positive solutions of multi-point boundary value problem of fractional diﬀerential equation, Arab Journal of Mathematical Sciences., vol. 21, no. {bf{2}} 2015, pp. 225–-236.

Mainardi, F., Fractional calculus: some basic problems in continuum and statistical mechanics. In: Carpinteri, CA, Mainardi, F (eds.) Fractal and Fractional Calculus in Continuum Mechanics. Springer., Vienna (1997).

Metzler, F., Schick, W., Kilian, HG., Nonnenmache, TF., Relaxation in filled polymers: a fractional calculus approach. J. Chem. Phys., {bf{103}}(1995), 7180--7186.

Nyamoradi, N., Existence of solutions for multi-point boundary value problems for fractional differential

equations, Arab J. Math. Sci., {bf{18}} (2012), 165–-175.

Oldham, K.B., Spanier, J., The Fractional Calculus, Academic Press, New York, London, 1974.

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

Pu, R.,Zhang, X., Cui, Y., Li, P., Wang, W., Positive solutions for singular semipositone fractional diferential equation subject to multipoint boundary conditions, Journal of Function Spaces., vol. 2017, Article ID 5892616, 8 pages, 2017

Ji, Y.D., Guo, Y.P., Qiu, J.Q., Yang, L.Y., Existence of positive solutions for a boundary value problem of nonlinear fractional diﬀerential equations, Advances in Diﬀerence Equations., vol. 2015, article 13, 2015.

Ross B., (ed.), The Fractional Calculus and its Applications, Lecture Notes in Mathematics, Vol. 475, Springer-Verlag, Berlin, 1975.

Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integral and Derivatives (Theory and Applications), Gordon and Breach, Switzerland, 1993.

Shah, K., Zeb, S., Khan, R. A., Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations, Computational Methods for Differential Equations.,

Vol. 5, No. {bf{2}} (2017), pp. 158--169.

Sun, Y., Zhao, M., Positive solutions for a class of fractional differential equations with integral boundary conditions. Appl. Math. Lett., {bf{34}} (2014), 17--21.

Tariboon, J., Ntouyas, S.K., Sudsutad, W., Positive solutions for fractional differential equations with three-point multi-term fractional integral boundary conditions, Adv. Difference Equ., 2014 (2014), 17 pages.1

Wang, Y., Liang S., Wang, Q., Multiple positive solutions of fractional-order boundary value problem with integral boundary conditions. J. Nonlinear Sci. Appl., {bf{10}} (2017), 6333–-6343.

Webb, J.R.L., Nonlocal conjugate type boundary value problems of higher order. Nonlinear Anal., {bf{71}}(2009), 1933--1940.

Zhou L., Jiang, W., Positive solutions for fractional differential equations with multi-point boundary value problems. Journal of Applied Mathematics and Physics., {bf{2}} (2014), 108--114.

DOI: http://dx.doi.org/10.24193/subbmath.2021.4.08

### Refbacks

- There are currently no refbacks.