Similarity solutions of fractional parabolic boundary value problems with uncertainty

Abstract We use similarity method to solve nonlinear fractional order fuzzy parabolic boundary value problem with Caputo fractional derivative. The fractional order fuzzy parabolic equation is converted into fuzzy fractional differential equation. Schauder’s fixed point theorem is used to derive the existence results. Finite difference method is used to obtain the numerical results. Examples are provided to justify the results.

[1]  J. Nieto,et al.  Invariant solutions of hyperbolic fuzzy fractional differential equations , 2020 .

[2]  Bancha Panyanak.  On the Ishikawa iteration processes for multivalued mappings in some CAT(κ) spaces , 2014 .

[3]  Tofigh Allahviranloo,et al.  SOLVING FUZZY FRACTIONAL DIFFERENTIAL EQUATIONS BY FUZZY LAPLACE TRANSFORMS , 2012 .

[4]  Roman Cherniha,et al.  Lie symmetries of nonlinear boundary value problems , 2010, 1012.5606.

[5]  Heriberto Román-Flores,et al.  Embedding of level-continuous fuzzy sets on Banach spaces , 2002, Inf. Sci..

[6]  Vasile Lupulescu,et al.  On the fractional differential equations with uncertainty , 2011 .

[7]  Sahin Emrah Amrahov,et al.  Solution of linear differential equations with fuzzy boundary values , 2014, Fuzzy Sets Syst..

[8]  Monika Zecová,et al.  Heat conduction modeling by using fractional-order derivatives , 2015, Appl. Math. Comput..

[9]  X. Guo,et al.  Fuzzy approximate solutions of second-order fuzzy linear boundary value problems , 2013 .

[10]  Min Qi,et al.  A reproducing kernel method for solving nonlocal fractional boundary value problems with uncertainty , 2017, Soft Comput..

[11]  Changpin Li,et al.  Finite difference Methods for fractional differential equations , 2012, Int. J. Bifurc. Chaos.

[12]  Ali Vahidian Kamyad,et al.  Modified fractional Euler method for solving Fuzzy Fractional Initial Value Problem , 2013, Commun. Nonlinear Sci. Numer. Simul..

[13]  Xiaoping Xue,et al.  Two-point boundary value problems of uncertain dynamical systems , 2011, Fuzzy Sets Syst..

[14]  Yury F. Luchko.  Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation , 2011 .

[15]  Wenjie Gao,et al.  Existence of solutions for nonlocal p-Laplacian thermistor problems on time scales , 2013 .

[16]  Hüseyin Koçak,et al.  Similarity solutions of nonlinear third-order dispersive PDEs: The first critical exponent , 2017, Appl. Math. Lett..

[17]  Omar Abu Arqub,et al.  Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: A new iterative algorithm , 2015, J. Comput. Phys..

[18]  Tayebeh A. Bidgoli,et al.  On the existence and uniqueness of solutions for fuzzy fractional differential equations , 2017 .

[19]  Sadia Arshad.  On Existence and Uniqueness of Solution of Fuzzy Fractional Differential Equations , 2013 .

[20]  Omar Abu Arqub,et al.  Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions , 2017, Comput. Math. Appl..

[21]  Juan J Nieto,et al.  Schauder fixed-point theorem in semilinear spaces and its application to fractional differential equations with uncertainty , 2014 .