A POSITIVE SOLUTION OF MIXED NON-LINEAR FRACTIONAL DELAY DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS
Received:April 19, 2022  Revised:August 10, 2022
Key Words: 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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Dayanand Kalyan Vyavahare School of Computational Sciences, PAH Solapur University, Solapur At/Post-Bhutashte, Tahsil- Madha, District-Solapur
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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.
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