Topological Degree Theory and Ulam’s Stability Analysis of a Boundary Value Problem of Fractional Differential Equations

Amjad Ali (), Kamal Shah () and Yongjin Li ()
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Amjad Ali: Government Postgraduate Jehanzeb College Saidu Sharif Mingora Swat, Department of Mathematics
Kamal Shah: University of Malakand, Department of Mathematics
Yongjin Li: Sun Yat-sen University, Department of Mathematics

A chapter in Frontiers in Functional Equations and Analytic Inequalities, 2019, pp 73-92 from Springer

Abstract: Abstract In this article, we study the existence and uniqueness of positive solution to a class of nonlinear fractional order differential equations with boundary conditions. By using fixed point theorems on contraction mapping together with topological degree theory, we investigate some sufficient conditions in order to obtain the existence and uniqueness of positive solution for the considered problem. Further we also investigate different kinds of Ulam stability for the considered problem. Moreover, we also provide an example to justify the whole results.

Keywords: Fractional differential equations; Caputo’s fractional derivative; Fixed point theorems; Existence and uniqueness; Arzela Ascali; Contraction mapping; Ulam’s stability; 26A33; 26A42; 34A08 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-28950-8_4

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DOI: 10.1007/978-3-030-28950-8_4

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