Research article

Nonlinear fractional boundary value problem with not instantaneous impulse

  • Received: 24 December 2016 Accepted: 25 May 2017 Published: 22 June 2017
  • In this article, the main focus is to propose the solution for the nonlinear fractional boundary system with non-instantaneous impulse under some weak conditions. By applying well known classical fixed point theorems, we obtained the existence and uniqueness outcomes of the solution for the proposed problem. Moreover, an example is also discussed to explain the present work.

    Citation: Vidushi Gupta, Jaydev Dabas. Nonlinear fractional boundary value problem with not instantaneous impulse[J]. AIMS Mathematics, 2017, 2(2): 365-376. doi: 10.3934/Math.2017.2.365

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  • In this article, the main focus is to propose the solution for the nonlinear fractional boundary system with non-instantaneous impulse under some weak conditions. By applying well known classical fixed point theorems, we obtained the existence and uniqueness outcomes of the solution for the proposed problem. Moreover, an example is also discussed to explain the present work.


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    [1] Kilbas A A, Srivastava H M, Trujillo J J, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
    [2] Miller K S, Ross B, An Introduction to the Fractional Calculus and Differential Equations, Wiley, New York, 1993.
    [3] Oldham K B, Spanier J, The Fractional Calculus, Academic Press, New York, 1974.
    [4] Podlubny I, Fractional Differential Equation, Academic Press, San Diego, 1999.
    [5] Samko S G, Kilbas A A, Marichev O I, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.
    [6] Li P, Xu C J, Mild solution of fractional order differential equations with not instantaneous impulses, Open Math, 13 (2015), 436-443.
    [7] Yu X, (2015) Existence and β-Ulam-Hyers stability for a class of fractional di erential equations with non-instantaneous impulses, Advances in Difference Equations, 2015.
    [8] Gupta V, Dabas J, Existence Results for a Fractional Integro-Differential Equation with Nonlocal Boundary Conditions and Fractional Impulsive Conditions, Nonlinear Dynamics and Systems Theory, 15 (2015), 370-382.
    [9] Gupta V, Dabas J, Existence of solution for fractional impulsive integro-differential equation with integral boundary conditions, Func. Anal.-TMA 1 (2015), 56-68.
    [10] Gupta V, Dabas J, Fractional Functional Impulsive Differential Equation with Integral Boundary Condition, Springer proceedings of Mathematical Analysis and its Applications (2014), 417-428.
    [11] Wang J, Li X, Periodic BVP for integer/fractional order nonlinear differential equations with noninstantaneous impulses, J. Appl. Math. Comput., 46 (2014), 321-334.
    [12] Lin Z, Wang J, WeiW, Multipoint BVPs for generalized impulsive fractional differential equations, Applied Mathematics and Computation, 2015.
    [13] Wang J, Zhou Y, Feckan M, On recent developments in the theory of boundary value problems for impulsive fractional differential equations, Comput. Math. Appl., 64 (2012), 3008-3020.
    [14] Hernandez E, O'Regan D, On a new class of abstarct impulsive differential equations, Proceedings of the American Mathematical Society, 141 (2012), 1641-1649.
    [15] Kumar P, Pandey D N, Bahuguna D, On a new class of abstract impulsive functional differential equations of fractional order, J. Nonlinear Sci. Appl., 7 (2014), 102-114.
    [16] Pierri M, O'Regan D, Rolnik V, Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses, Applied Mathematics and Computation, 219 (2013), 6743-6749.
    [17] Gautam G R, Dabas J, Mild solution for fractional functional integro-differential equation with not instantaneous impulse, Malaya J. Mat., 2 (2014), 428-437.
    [18] Agarwal R, Meehan M, O'Regan D, Fixed point theory and applications, Cambridge tracts in mathematics, New York (NY): Cambridge University Press, 2001.
    [19] Feckan M, Zhou Y, Wang J, On the concept and existence of solution for impulsive fractional differential equations, Comm. Nonl. Sci. Num. Sum., 17 (2012), 3050-3060.
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  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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