EXISTSTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR A CLASS OF BOUNDARY VALUE PROBLEM INCLUDING FRACTIONAL DIFFERENTIAL EQUATION

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AHMADKHANLU ASGHAR

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ISSN: 2588-4824

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Journal: MATHEMATICAL RESEARCHES Year:2017 | Volume:3 | Issue:1 Page(s): 1-10

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Title

EXISTSTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR A CLASS OF BOUNDARY VALUE PROBLEM INCLUDING FRACTIONAL DIFFERENTIAL EQUATION

Author(s)

AHMADKHANLU ASGHAR | Issue Writer Certificate

Keywords

BOUNDARY VALUE PROBLEMQ2

FRACTIONAL DIFFERENTIAL EQUATIONSQ1

REIMMAN LIOUVILLE FRACTIONAL DERIVATVEQ1

FIXED POINT THEOREMQ1

Abstract

In this paper we investigate a kind of BOUNDARY VALUE PROBLEM involving a fractional differential equation. We study the existence of positive solutions of the problem that fractional derivative is the Reimann-Liouville fractional derivative. At first the green function is computed then it is proved that the green function is positive. We present necessary and sufficient conditions for existence of positive solution by calculating supremum of integral of green function over the solution interval and by use of some expansions of contraction mapping that are presented recently. For this purpose, at first the existence and uniqueness of solution for the problem, by use of existence of lower solution for the problem and expansion of contraction mapping on ordered space, is proved. Then by use of another expansion of contraction mapping on ordered spaces, the existence and uniqueness of positive solution is proved. Also, an example is presented to illustrate the proven results.

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APA: Copy

AHMADKHANLU, ASGHAR. (2017). EXISTSTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR A CLASS OF BOUNDARY VALUE PROBLEM INCLUDING FRACTIONAL DIFFERENTIAL EQUATION. MATHEMATICAL RESEARCHES, 3(1), 1-10. SID. https://sid.ir/paper/260796/en

Vancouver: Copy

AHMADKHANLU ASGHAR. EXISTSTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR A CLASS OF BOUNDARY VALUE PROBLEM INCLUDING FRACTIONAL DIFFERENTIAL EQUATION. MATHEMATICAL RESEARCHES[Internet]. 2017;3(1):1-10. Available from: https://sid.ir/paper/260796/en

IEEE: Copy

ASGHAR AHMADKHANLU, “EXISTSTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR A CLASS OF BOUNDARY VALUE PROBLEM INCLUDING FRACTIONAL DIFFERENTIAL EQUATION,” MATHEMATICAL RESEARCHES, vol. 3, no. 1, pp. 1–10, 2017, [Online]. Available: https://sid.ir/paper/260796/en

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