Approximate Solution of Fuzzy Caputo's-Katugampola differential equation with order 0
DOI:
https://doi.org/10.31185/wjps.593Keywords:
Caputo- Katugampla , Riemann-Liouville, Gram-Schmidt, reproducing kernel, Riemann- HadamardAbstract
In this paper that some of fuzzy second order Caputo's- Katugampola fractional which included also the first order Caputo's- Katugmpola fractional have been presented with analytic interesting result to explain the solution in fuzzy real numbers and distinguish space included the type of functions which suitable to the problem formulations which are under studied. all the fuzzy results are supported the numerical solutions that which used later on. The interesting illustrative examples for application some classes of fuzzy Caputo- Katugampla fractional order differential equations with and explained their systems (n, m) where n, m=1,2, moreover the tables of different parameters and different fractional orders have been given in details and different values of fuzzy parameter. All tables are represented by figures that given in first time. Coupled figures for each table refer to lower and upper of fuzzy solution. The algorithm of reproducing kernel Hilbert space are used with their steps and Gram-Schmidt orthogonalization process to obtain the approximate solution.
References
Abu Arqub O., Approximate solution of DASs with nonclassical boundary condition using Novel Reproducing Kernel Algorithm, Fundamenta informaticae 146(2016),231-254.
Abu Arqub O., Al-smadi M. and Shawagfeh N., Solving Fredholm intgro- Differential equation using reproducing kernel Hilbert space method, Applied Mathematics and Computation vol.219, no.17, pp.8938-8948,2013.
Abu Arqub O., Al-smadi M. and Momani S., Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integrodifferential equation, Abstract and Applied Analysis, vol.2012, Article ID839836,16 pages, 2012. ).
Ahmadian A., Suleiman M. and Salahshour S., An operational matrix based on legendre polynomials for solving fuzzy fractional-order differential equation, Hindawi publishing Corporation Abstract and Applied Analysis Vol.2013, Article ID 505903,29pages.
Almeida R. and Maliknowska A.B., fractional differential equation with dependence on the Caputo-katugampola derivative, article Jul, 2016.
AL-Smadi M.and Arqub A O., Computational algorithm for Solving fredholm time-fractional partial integrodifferential equation of dirichlt function type with error estimates, Applied mathematics and compution 342(2019)280-294.
Azarnavid B., Parvaneh F. and Abbasbandy S., Picard-reproducing kernel Hilbert space method for solving generalized singular nonlinear Lane-Emden type equation, mathematical Modelling and Anlysis, vol.20, no.6, pp.754-767,2015.
Bushnaq S., Maayah S., Momani S., and Alsaedi A., reproducing kernel Hilbert space method for solving systems of fractional integrodifferential equation, Abstract and Applied Analysis, vol.2014, Article ID 103016,6 pages,2014.
Caputo M., Fabrizio, A new definition of fractional derivative with singular kernel. Prog. Fract Differ. Appl.1(2015)73-85
Chen X., Gu H. and Wang X., Existence and uniqueness for fuzzy differential derivative, Chen et al. Advances in difference equations (2020) 2020:241.
Fahd J., Thabet A. and Dumitru B., On the generalized fractional derivative and their Caputo modification, Journal of Nonlinear Sciences and Application., 10(2017),2607-2619.
Geng F. and Cui M., Solving a nonlinear system of second order boundary value problems, Journal of mathematical Analysis and Application, vol.327, no.2, pp.1167-1181,2007.
Gumah G.N., Naser M.F.M., AL-smadi M.and AL-omari S.K., Application of reproducing kernel Hilbert space method for solving second-order fuzzy Volterra integro-differential equation,Gumah et al, Advances in difference equation (2018)2018:475.
Gupta A.K. and Ray S.S., On the solution of time-fractional KdV- burgers equation using petrov-galerkin method for propagation of long wave in shallow water, Chaos Solitons. Fractals.Vol.116(2018)376-380.
Haq E.U., Hassan Q.M.U., Ahmad J. and Ehsan K., fuzzy solution of system of fuzzy fractional problems using a reliable method, Alexandria Engineering Journal (2022) 61,305-3058.
Hassan J.S. and Grow D., stability and approximation of solution in new reproducing kernel Hilbert space on a semi-infinite domain, Wiley, Nath meth Appsei 2021:1-41
Hassan S., Alawneh A., AL-Momani M. and Momani S., second order fuzzy fractional differential equation undr Caputo’s H-differentiability, Appl.math.inf. Sci.11. No.6,1597-1608(2017).
Holel M.A., The classes Optimality of Nonlinear fractional Differential Dynamical Control Equation, thesis, mustansiriyah university, college of education,2023.
Inc M., Akgul A., and Geng F., Reproducing kernel Hilbert space Bratu’s problem, Submited on December 27,2012, pp 1-20.
Inc M., Akgul A., and Geng F., Reproducing kernel Hilbert space Bratu’s problem, Bulletin of the Malaysian Mathematical Sciences Society, vol.38, no.1, pp.271—287,2015.
Ineirat A.L.L., Numerical method for solving fuzzy system of linear equation, thesis, An-najah national university, Nablus Palestine.
Javan S.F, Abbasband.S. and Araghi M.A.F., Application reproducingkernel Hilbert space method for solving a class of nonlinear integral equation, Hindawi mathematical problem in engineering Vol.2017.Artical ID:7498136,10 pages
Jiang Y. and Tian T., Numerical solution nonlinear integro-differential equation of fractional order by the reproducing kernel method Applied mathematical modeling 39(2015)4871-4876.
Katugampola U.N., New approach to generalized fractional integral, APPl. Math. Comput.218(2011),860-8656.
[25] Katugampola U.N., A New approach to generalized fractional derivatives, Bull. Math. Anal.App.6(2014),1—15
Katugampola U.N., Existence and uniqueness result for a class of Generalized fractional differential equation, submitted, ariXiv:14115229v1 [math.CA]7Nov 2014.
Kilbas A.A. and Saigo M., On solution of nonlinear Abel Volterra integral equation, Journal of Mathematical Analysis and Application, vol.229, no.1, pp.41-60,1999.
Kilbas A.A., Srivastava H.M. and Trujillo J.J, Theory and Application of Fractional differential equation, North=Holland Mathematics Studies, 204, Elsevier Science B.V, Amsterdam, 2006.
Minggen C., and Zhongxing D., On the best Operator of interpolation, Mathematica Numerica Sinica, vol.8, no.2, pp.209-216,1986.
Minggen C., and Yingzhen L., Nonlinear Numerical Analysis in the Reproducing kernel Hilbert space,Nova Science , New York, NY, USA, 2009.
Morales-Delgado V.F., Gomez-Aguilar J.F., Yepez-Martiinez, H., Baleanu D., Escobar-Jimenez R.F and Olivares-peregrino V.H., Adv.Differ. Equ. 2016(2016)1—17.
Podlubny I., Fractional differential equation, Mathematics in Science and Engineering, 198.dam,2006
Rashid S., Ashraf R. and Hammouch Z., New generalized fuzzy trans-form computations for solving fractional partial differential equation arising in oceanography, journal of ocean engineering and science8 (2023) 55-78.
Ray S.S. and Sagar B., Numer. Method Partial Differ. Equ. (2022)1-11.
Saad K.M., Atangana A. and Baleanu D., New fractional derivative with non-singular kernel applied to the burgers equation,Chaos 28(2018)063109.
Saadeh R., Numerical algorithm to solve a coupled system of fractional Order using a novel reproducing kernel method, Alexandria Engineering Journal (2021),60,4583-4591.64
Sakar M.G., Iterative reproducing kernel Hilbert space method for Riccati differential equation, journal computational and Applied mathematics 309(2019) 163-174.
Samko S.G., Kilbas A.A. and Marichev O.I, fractional integral and Derivatives, translated from the 1987 Russian original, Grordon and Breach, Yverdon, 1993.
Verma L., Meher R., Avazzodh Z. and Nikan O., solution for generalized Fuzzy fractional Kortewege-de varies equation using a robust fuzzy double parametric approach, Journal of Ocean Engineering and science8 (2023)602-622
Yang L. and Cui M., New algorithm for a class of nonlinear integro- Differential equation in the Reproducing Kernel space, Applied Mathematica and Computation, vol.174, no.2, pp.942-960,2006.
Yang, X.J. (2021). Theory and Applications of Special functions for Scientists and Engineers. Sringer Singapore, New York, USA.
Zimmermann H.J., fuzzy theory and its Application Third Edition 1996 by Kluwer academic published.
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