A Positive Solution of Mixed Non-Linear Fractional Delay Differential Equations with Integral Boundary Conditions
Received:April 19, 2022  Revised:August 19, 2022
Key Words: Guo-Krasnoseleskii's fixed point theorem   Banach contraction principle   mixed non-linear fractional delay differential equations   integral boundary conditions   existence   uniqueness  
Fund Project:Supported by Council of Scientific and Industrial Research-Human Resource Development Group (CSIR-HRDG) (Grant No.09/0990(11223)/2021-EMR-I).
Author NameAffiliation
Dayanand K. VYAVAHARE Department of Mathematics, Punyashlok Ahilyadevi Holkar Solapur University, Solapur-413255, India 
Vinod V. KHARAT Department of Mathematics, N. B. Navale Sinhgad College of Engineering, Solapur-413255, India 
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      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.
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