Numerical Results for Linear Sequential Caputo Fractional Boundary Value Problems

Bhuvaneswari Sambandham, Aghalaya S. Vatsala and Vinodh K. Chellamuthu
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Bhuvaneswari Sambandham: Department of Mathematics, Dixie State University, St. George, UT 84770, USA
Aghalaya S. Vatsala: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
Vinodh K. Chellamuthu: Department of Mathematics, Dixie State University, St. George, UT 84770, USA

Mathematics, 2019, vol. 7, issue 10, 1-10

Abstract: The generalized monotone iterative technique for sequential 2 q order Caputo fractional boundary value problems, which is sequential of order q , with mixed boundary conditions have been developed in our earlier paper. We used Green’s function representation form to obtain the linear iterates as well as the existence of the solution of the nonlinear problem. In this work, the numerical simulations for a linear nonhomogeneous sequential Caputo fractional boundary value problem for a few specific nonhomogeneous terms with mixed boundary conditions have been developed. This in turn will be used as a tool to develop the accurate numerical code for the linear nonhomogeneous sequential Caputo fractional boundary value problem for any nonhomogeneous terms with mixed boundary conditions. This numerical result will be essential to solving a nonlinear sequential boundary value problem, which arises from applications of the generalized monotone method.

Keywords: sequential Caputo fractional derivative; fractional boundary value problem; Mittag-Leffler Function; Green’s function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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