924
Views
14
CrossRef citations to date
0
Altmetric
Research Articles

Existence results of solution for fractional Sturm–Liouville inclusion involving composition with multi-maps

ORCID Icon & ORCID Icon
Pages 721-733 | Received 09 Mar 2020, Accepted 12 May 2020, Published online: 28 May 2020

References

  • Iqbal M , Seadawy AR , Lu D. Construction of solitary wave solutions to the nonlinear modified Kortewege-de Vries dynamical equation in unmagnetized plasma via mathematical methods. Mod Phys Lett A. 2018;33(32):1850183.
  • Iqbal M , Seadawy AR , Lu D. Dispersive solitary wave solutions of nonlinear further modified Korteweg-de Vries dynamical equation in an unmagnetized dusty plasma. Mod Phys Lett A. 2018;33(37):1850217.
  • Iqbal M , Seadawy AR , Lu D. Applications of nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod and new solitary wave solutions. Mod Phys Lett B. 2019;33(18):1950210.
  • Iqbal M , Seadawy AR , Khalil OH , et al. Propagation of long internal waves in density stratified ocean for the (2+1)-dimensional nonlinear Nizhnik-Novikov-Vesselov dynamical equation. Res Phys. Mar 2020;16:102838.
  • Lu D , Seadawy AR , Iqbal M. Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations. Open Phys. 2018;16:896–909.
  • Seadawy AR , Iqbal M , Lu D. Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized Kadomtsev-Petviashvili modified equal width dynamical equation. Comput Math Appl. Dec 2019;78(11):3620–3632.
  • Seadawy AR , Iqbal M , Lu D. Propagation of long-wave with dissipation and dispersion in nonlinear media via generalized Kadomtsive-Petviashvili modified equal width-Burgers equation. Indian J Phys. May 2019;94:675–694.
  • Seadawy AR , Iqbal M , Lu D. Construction of soliton solutions of the modify unstable nonlinear Schrodinger dynamical equation in fiber optics. Indian J Phys. Jun 2019;94:823–832.
  • Iqbal M , Seadawy AR , Lu D. Construction of a weakly nonlinear dispersion solitary wave solution for the Zakharov–Kuznetsov-modified equal width dynamical equation. Indian J Phys. 2019;93:1–10.
  • Seadawy AR , Iqbal M , Lu D. Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg-de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma. Phys A. Apr 2020;544:123560.
  • Seadawy AR , Iqbal M , Lu D. Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity. J Taibah Univ Sci. 2019;13(1):1060–1072.
  • Iqbal M , Seadawy AR , Lu D , et al. Construction of bright–dark solitons and ion-acoustic solitary wave solutions of dynamical system of nonlinear wave propagation. Mod Phys Lett A. 2019;34(37):1950309.
  • Lu D , Seadawy AR , Iqbal M. Mathematical methods via construction of traveling and solitary wave solutions of three coupled system of nonlinear partial differential equations and their applications. Res Phys. Dec 2018;11:1161–1171.
  • Seadawy AR , Lu D , Iqbal M. Application of mathematical methods on the system of dynamical equations for the ion sound and Langmuir waves. Pramana J Phys. 2019;93(1):10.
  • Kilbas AA , Srivastava HM , Trujillo JJ. Theory and applications of fractional differential equations. Amsterdam: Elsevier Science, BV; 2006. (North Holland Mathematics Studies; vol. 204).
  • Lan KQ , Lin W. Positive solutions of systems of Caputo fractional differential equations. Commun Appl Anal. 2013;17(1):61–86.
  • Salem A , Alzahrani F , Alnegga M. Coupled system of non-linear fractional Langevin equations with multi-point and nonlocal integral boundary conditions. Math Probl Eng. 2020;2020: Article ID 7345658 | 15 pages.
  • Salem A , Alzahrani F , Alghamdi B. Langevin equation involving two fractional orders with three-point boundary conditions. Differ Integr Equ. 2020;33(3-4): 163–180.
  • Salem A , Alzahrani F , Almaghamsi L. Fractional Langevin equation with nonlocal integral boundary condition. Mathematics. 2019;7(5):402.
  • Salem A , Aghamdi B. Multi-point and anti-periodic conditions for generalized Langevin equation with two fractional orders. Fractal Fractional. 2019;3(4):51.
  • Zhou Y. Attractivity for fractional differential equations in Banach space. Appl Math Lett. 2018;75:1–6.
  • Zhou Y , He JW , Ahmad B. Existence and attractivity for fractional evolution equations. Discrete Dynamics in Nature and Society. Hindawi; 2018.
  • Zhou Y. Attractivity for fractional evolution equations with almost sectorial operators. Fract Calc Appl Anal. 2018;21(3):786–800.
  • Ahmad B , Alsaedi A , Ntouyas SK. Hadmard-type fractional differentional equations, inclusions and inequalities. Switzerland (Gewerbestrasse 11, 6330 Cham ): Springer International Publishing AG; 2017.
  • Kamenskii M , Obukhovskii V , Petrosyan G , et al. Existence and approximation of solutions to nonlocal boundary value problems for fractional differential inclusions. Fixed Point Theory Appl. 2019;2019(1):1–21.
  • Kamenskii M , Obukhovskii V , Petrosyan G , et al. On semilinear fractional order differential inclusions in Banach spaces. Fixed Point Theory Appl. 2017;18(1):269–292.
  • Kamenskii M , Obukhovskii V , Petrosyan G , et al. Boundary value problems for semilinear differential inclusions of fractional order in a Banach space. Appl Anal. 2018;97(4):571–591.
  • Gerald T. Mathematical methods in quantum mechanics. Rhode Island : American Mathematical Society; 2009.
  • El-Sayed AMA , Gaafar FM. Existence and uniqueness of solution for Sturm–Liouville fractional differential equation with multi-point boundary condition via Caputo derivative. Adv Differ Equ. 2019;2019(1):1–17. Nature Publishing Group.
  • Liu X , Liu Z. Existence results for fractional differential inclusions with multivalued term depending on lower-order derivative. Abstr Appl Anal. 2012;2012: Article ID 423796 | 24 pages. Hindawi.
  • Ahmad B , Ntouyas SK. Fractional differential inclusions with fractional separated boundary conditions. Fract Calculus Appl Anal. 2012;15(3):362–382.
  • Ahmad B , Ntouyas SK. Existence of solutions for fractional differential inclusions with nonlocal strip conditions. Arab J Math Sci. 2012;18(2):121–134.
  • Cernea A. On a multi point boundary value problem for a fractional order differential inclusion. Arab J Math Sci. 2013;19(1):73–83.
  • Fu X. Existence results for fractional differential inclusions with three-point fractional integral boundary conditions. Adv Differ Equ. 2013;2013(1):304.
  • Kisielewicz M. Differential inclusions and optimal control. Dordrecht, The Netherlands: Kluwer; 1991.
  • Castaing C , Valadier M. Convex analysis and measurable multifunctions. Vol. 580. Berlin, Heidelberg, New York : Springer; 2006.
  • Deimling K. Multivalued differential equations. Berlin: Walter De Gruyter; 1992.
  • Al-Gwaiz M , Al Sanousi S. Elements of real analysis. Boca Raton, London, New York : Champan and Hall Book, CRC Press: Taylor & Francis Group; 2006.
  • Kelley JL. General Topology. New York (Mineola ): Dover Publications, INC.; 2017.
  • Fierroa R , Martneza C , Morales CH. Carathé odory selections for multivalued mappings. Nonlinear Anal: Theory, Methods Appl. 2006;64(6):1229–1235.
  • Davis JG. A graphical method for function composition. Teaching Math Appl. 2000;19:154–157.
  • Tolstonogov AA. Differential inclusions in a Banach space. Dordrecht: Kluwer Academic; 2000.
  • Gorniewicz L. Topological fixed point theory of multivalued mappings. Dordrecht: Kluwer Academic; 1999. (Mathematics and its Applications; vol. 495).
  • Hu S , Papageorgiou NS. Handbook of multivalued analysis. Vol. 1. Dordrecht : Kluwer Academic; 1997.
  • Lasota A , Opial Z. An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull Acad Polon Sci Ser Sci Math Astron Phys. 1965;13:781–786.
  • Granas A , Dugundji J. Fixed point theory. New York: Springer; 2003.
  • Singh SP. Nonlinear functional analysis and its application. Vol. 173. Maratea, Italy : NATO Scientific Affairs Division; 1985. p. 187–194.
  • Covitz H , Nadler SB. Multivalued contraction mappings in generalized metric spaces. Isr J Math. 1970;8:5–11.
  • Hildebrand FB. Methods of applied mathematics. 2nd ed. New York : Dover Publications, INC.; 2012.
  • Kevorkian J , Cole JD. Perturbation methods in applied mathematics. (Berlin and New York): , Appl. Math. Sci., Springer- Verlage ; 1981.
  • Ouahab A. Some results for fractional boundary value problem of differential inclusions. Nonlinear Anal: Theory Methods Appl. 2008;69(11):3877–3896.
  • Bressan A , Colombo G. Extensions and selections of maps with decomposable values. Stud Math. 1988;90(1):69–86.
  • Shang Y. Fixed-time group consensus for multi-agent systems with nonlinear dynamics and uncertainties. IET Control Theory Appl. 2018;12(3):395–404. School of Mathematical Sciences.
  • Bhat SP , Bernstein DS. Finit time stability of continuous autonomous systems. SIAM J Control Optim. 2000;38(3):751–757. Society for Industrial and Applied Mathematics.
  • Moulay E , Perruquetti W. Finite time stability of differential inclusions. IMA J Math Control. May 2005;22(4):465–475.