Study Boundary Problem with Integral condition for Fractional Differential Equations

Abdulkader, Nawal Aziz; Adnan, Nadia

doi:10.33899/edusj.2020.126471.1038

	Study Boundary Problem with Integral condition for Fractional Differential Equations
Journal of Education and Science
Article 18, Volume 29, Issue 3, 2020, Pages 237-245 PDF (351.15 K)
Document Type: Research Paper
DOI: 10.33899/edusj.2020.126471.1038
Authors
Nawal Aziz Abdulkader¹; Nadia Adnan^* ²
¹Mathematics Department, College of Education for Pure Science, Mosul University, Mosul< Iraq
²Mathematics Dept , Education Colloge for pur science , Mosul University , Mosul-Iraq
Abstract
In last many years ago there was a great interest in studying the existence of positive solutions for fractional differential equations. Many authors have considered the existence of positive solutions of non-linear differential equations of non-integer order with integral boundary value conditions using fixed point theorems. G.wang etal(2012)in vest gated the following fractional differential equation 〖^c〗D^α W(t)+f(t,W(t))=0,0 λ is a positive number (0 < λ < 2),〖^C〗D^αis the standard Caputo fractional derivative obtained his results by means of Guo-krosnosel'skii theorem in a cone also A.Cabada etat (2013) established the following non-linear fractional differential equation with integral boundary value conditions D^α W(t)+f(t,W(t))=0 ,00 ,λ≠α ,〗 D^αis Riemann –Liovuville standard fractional derivative and f is a continuous function the results was based on Guo-krasnosel'skii fixed point theorem in a cone . This paper we investigate the existence results of a positive solution for integral boundary value conditions of the following system of equations: 〖^c〗D^β h(t)+k(t,h(t))=0 ,t∈(0,1) h(0)=h^' (0)=h^''' (0)=0 ,h(1)=δ∫_0^1▒h(n)dn where 3< β≤4 ,δ is a positive number , δ≠3 ,〖^C〗D^β denotes Caputo standard derivative and k is a continuous function.Our work based on Banach's and Schauder's theorem.
Keywords
Fractional differential Equation,,; ,،,؛Integral boundary value Conditions,,; ,،,؛Schauder's theorem,,; ,،,؛Green function

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