On the Parametrization of Caputo-Type Fractional Differential Equations with Two-Point Nonlinear Boundary Conditions

Nazım I. Mahmudov, Sedef Emin and Sameer Bawanah
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Nazım I. Mahmudov: Department of Mathematics, Faculty of Art and Science, Eastern Mediterranean University, Famagusta 99628, T. R. North Cyprus, 10 Mersin, Turkey
Sedef Emin: Department of Mathematics, Faculty of Art and Science, Eastern Mediterranean University, Famagusta 99628, T. R. North Cyprus, 10 Mersin, Turkey
Sameer Bawanah: Department of Mathematics, Faculty of Art and Science, Eastern Mediterranean University, Famagusta 99628, T. R. North Cyprus, 10 Mersin, Turkey

Mathematics, 2019, vol. 7, issue 8, 1-23

Abstract: In this paper, we offer a new approach of investigation and approximation of solutions of Caputo-type fractional differential equations under nonlinear boundary conditions. By using an appropriate parametrization technique, the original problem with nonlinear boundary conditions is reduced to the equivalent parametrized boundary-value problem with linear restrictions. To study the transformed problem, we construct a numerical-analytic scheme which is successful in relation to different types of two-point and multipoint linear boundary and nonlinear boundary conditions. Moreover, we give sufficient conditions of the uniform convergence of the successive approximations. Also, it is indicated that these successive approximations uniformly converge to a parametrized limit function and state the relationship of this limit function and exact solution. Finally, an example is presented to illustrate the theory.

Keywords: Caputo-type fractional differential equation; parametrized boundary conditions; numerical-analytic scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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