Existence of positive solution to a class of boundary value problems of fractional differential equations

	Existence of positive solution to a class of boundary value problems of fractional differential equations
Computational Methods for Differential Equations
مقاله 2، دوره 4، شماره 1، فروردین 2016، صفحه 19-29 اصل مقاله (134.94 K)
نوع مقاله: Research Paper
نویسندگان
Amjad Ali^* ؛ Kamal Shah؛ Rahmat Ali Khan
Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
چکیده
This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Thank to classical fixed point theorems of nonlinear alternative of Leray-Schauder and Banach Contraction principle, sufficient conditions are developed under which the proposed problem has at least one solution. An example has been provided to illustrate the main results.
کلیدواژه‌ها
Boundary value problem؛ Existence and uniqueness results؛ Fractional differential differential equations؛ Classical fixed point theorem

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