[1] Abramowitz M, Stegun I A. Hand Book of Mathematical Functions. New York: Dover, 1972
[2] Ang W T. A Method of Solution for the One-Dimentional Heat Equation Subject to Nonlocal Conditions. Southeast Asian Bulletin of Mathematics, 2002, 26: 185-191
[3] Be¨?lin S A. Existence of solutions for one-dimentional wave nonlocal conditions. Electron J Differential Equations, 2001, 200176): 1-8
[4] Bouziani A. Mixed problem with boundary integral conditions for a certain parabolic equation. J Appl Math Stochastic Anal, 1996, 9(3): 323-330
[5] Bouziani A. Solution forte d'un problème mixte avec une condition non locale pour une classe d'équations hyperboliques [Strong solution of a mixed problem with a nonlocal condition for a class of hyperbolic equations]. Acad Roy Belg Bull Cl Sci, 1997, 8: 53-70
[6] Sur un problème mixte avec uniquement des conditions aux limites intégrales pour une classe d'équations paraboliques. Maghreb Mathematical Review, 2000, 9(1/2): 55-70
[7] Bouziani A, Mechri R. The Rothe Method to a Parabolic Integro-differential Equation with a Nonclassical Boundary Conditions. Int Jour of Stochastic Analysis, Article ID 519684/16 page, doi: 10.1155/519684/(2010)
[8] Byszewski L. Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J Math Anal Appl, 1991, 162: 494-505
[9] Byszewski L. Theorems about the existence and uniqueness of continuous solutions of nonlocal problem for nonlinear hyperbolic equation. Appl Anal, 1991, 40: 173-180
[10] Byszewski L, Acka H. Existence of solutions of semilinear functional differential evolution nonlocal problems. Nonlinear Analysis, 1998, 34: 65-72
[11] Balachandran K, Park J Y. Existence of mild solution of a functional integrodifferential equation with nonlocal condition. Bulletin of the Korean Mathematical Society, 2001, 38: 175-182
[12] Balachandran K, Uchiyama K. Existence of solutions of quasilinear integrodifferential equations with nonlocal condition. Tokyo Journal of Mathematics, 2000, 23: 203-210
[13] Balachandran K, Park D G. Existence of solutions of quasilinear integrodifferential evolution equations in Banach spaces. Bulletin of the Korean Mathematical Society, 2009, 46: 691-700
[14] Balachandran K, Samuel F P. Existence of solutions for quasilinear delay integrodifferential equations with nonlocal condition. Electronic Journal of Differential Equations, 2009, 2009(6): 1-7
[15] N'Guérékata G M. A Cauchy problem for some fractional abstract differential equation with non local conditions. Nonlinear Analysis: Theory Methods and Applications, 2009, 70: 1873-6
[16] Balachandran K, Park J Y. Nonlocal Cauchy problem for abstract fractional semilinear evolution equations. Nonlinear Analysis: Theory Methods and Applications, 2009, 71: 4471-5
[17] Ahmad B. Some existence results for boundary value problems of fractional semilinear evolution equations. Electronic Journal of Qualitative Theory of Differential Equations, 2009, (28): 1-7
[18] Balachandran K, Trujillo J J. The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces. Nonlinear Analysis: Theory Methods and Applications, 2010, 72: 4587-93
[19] Elbeleze A A, K?l?çman A, Taib B M. Application of homotopy perturbation and variational iteration method for Fredholm integro-differential equation of fractional order. Abstract & Applied Analysis, 2012, 2012: 14 pages
[20] Elbeleze A A, K?l?çman A, Taib B M. Homotopy Perturbation Method for Fractional Black-Scholes European Option Pricing Equations Using Sumudu Transform. Mathematical Problems in Engineering, 2013, 2013: 7 pages
[21] Gordeziani D G, Avalishvili G A. Solution of nonlocal problems for one-dimensional oscillations of a medium. Mat Model, 2000, 12(1): 94-103
[22] Graver D P. Observing stochastic processes and aproximate transform inversion. Oper Res, 1966, 14: 4440-459
[23] Hassanzadeh H, Pooladi-Darvish M. Comparision of different numerical Laplace inversion methods for engineering applications. Appl Math Comp, 2007, 189: 1966-1981
[24] Kythe P K, Puri P. Computational methods for linear integral equation. New Orlans: Universty of New Orlans, 2002
[25] Kac?r J. Method of Rothe in Evolution Equations//Teubner-Texte zur Mathematik, Vol 80. Leipzig: BSB B. G. Teubner Verlagsgesellschaft, 1985
[26] Merad A. Adomian Decomposition Method for Solution of Parabolic Equation to Nonlocal Conditions. Int Journal of Contemp Math Sciences, 2011, 6(29/32): 1491-1496
[27] Merad A, Marhoune A L. Strong Solution for a High Order Boundary Value Problem with Integral Condition. Turk Jour Math, 2013, 37(3): 1-9
[28] Merazga N, Bouziani A. Rothe time-discretization method for a nonlocal problem arising in thermoelasticity. Journal of Applied Mathematics and Stochastic Analysis, 2005, 2005(1): 13-28
[29] Mesloub S, Bouziani A. Mixed problem with integral conditions for a certain class of hyperbolic equations. Journal of Applied Mathematics, 2001, 1(3): 107-116
[30] Pul'kina L S. A non-local problem with integral conditions for hyperbolic equations. Electron J Differential Equations, 1999, 1999(45): 1-6
[31] Pul'kina L S. On the solvability in L2 of a nonlocal problem with integral conditions for a hyperbolic equation. Differ Equ, 2000, 36(2): 316-318
[32] Pul'kina L S. A mixed problem with integral condition for the hyperbolic equation. Matematicheskie Zametki, 2003, 74(3): 435-445
[33] Stehfest H. Numerical Inversion of the Laplace Transform. Comm ACM, 1970, 13: 47-49
[34] Shruti A D. Numerical Solution for Nonlocal Sobolev-type Differential Equations. Electronic Journal of Differential Equations, 2010, 19: 75-83
[35] Wazwaz AM. A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equation. Appl Math and Comp, 2006, 181(2): 1703-1712 |