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A Positive Solution of Mixed Non-Linear Fractional Delay Differential Equations with Integral Boundary Conditions
作者姓名:Dayanand K. VYAVAHARE  Vinod V. KHARAT
作者单位:Department of Mathematics, Punyashlok Ahilyadevi Holkar Solapur University, Solapur-413255, India;Department of Mathematics, N. B. Navale Sinhgad College of Engineering, Solapur-413255, India
基金项目:Supported by Council of Scientific and Industrial Research-Human Resource Development Group (CSIR-HRDG) (Grant No.09/0990(11223)/2021-EMR-I).
摘    要:In this paper, we study mixed non-linear fractional delay differential equations with integral boundary conditions. We obtain an equivalence result between the proposed problem and non-linear Fredholm integral equation of the second kind. Further, we establish existence and uniqueness of positive solutions for the problem using Guo-Krasnoseleskii''s fixed point theorem and Banach contraction principle.

关 键 词:Guo-Krasnoseleskii''s  fixed  point  theorem    Banach  contraction  principle    mixed  non-linear  fractional  delay  differential  equations    integral  boundary  conditions    existence    uniqueness
收稿时间:2022/4/19 0:00:00
修稿时间:2022/8/19 0:00:00

A Positive Solution of Mixed Non-Linear Fractional Delay Differential Equations with Integral Boundary Conditions
Dayanand K. VYAVAHARE,Vinod V. KHARAT.A Positive Solution of Mixed Non-Linear Fractional Delay Differential Equations with Integral Boundary Conditions[J].Journal of Mathematical Research with Applications,2023,43(2):213-226.
Authors:Dayanand K VYAVAHARE  Vinod V KHARAT
Institution:Department of Mathematics, Punyashlok Ahilyadevi Holkar Solapur University, Solapur-413255, India; Department of Mathematics, N. B. Navale Sinhgad College of Engineering, Solapur-413255, India
Abstract:In this paper, we study mixed non-linear fractional delay differential equations with integral boundary conditions. We obtain an equivalence result between the proposed problem and non-linear Fredholm integral equation of the second kind. Further, we establish existence and uniqueness of positive solutions for the problem using Guo-Krasnoseleskii''s fixed point theorem and Banach contraction principle.
Keywords:Guo-Krasnoseleskii''s fixed point theorem  Banach contraction principle  mixed non-linear fractional delay differential equations  integral boundary conditions  existence  uniqueness
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