Indian Journal of Science and Technology

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Criteria on Existence of Solutions for Fractional Order Impulsive Differential System with Infinite Delay


Affiliations
1 Department of Mathematics, National Institute of Technology Raipur, Opp Ayurvedic College, GE Rd, Raipur – 492001, Chhattisgarh, India
 

The paper is mainly concerned with the existence and uniqueness of solution for a class of Cauchy initial value problem of fractional order with impulses and infinite delay. The criteria on existences and uniqueness are obtained via successive approximation and solution operator. Finally an example is given to support our main result.

Keywords

Caputo Fractional Derivative, Existence and Uniqueness, Fractional Impulsive Differential Equation, Infinite Delay
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  • Criteria on Existence of Solutions for Fractional Order Impulsive Differential System with Infinite Delay

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Authors

R. P. Pathak
Department of Mathematics, National Institute of Technology Raipur, Opp Ayurvedic College, GE Rd, Raipur – 492001, Chhattisgarh, India
Piyusha S. Somvanshi
Department of Mathematics, National Institute of Technology Raipur, Opp Ayurvedic College, GE Rd, Raipur – 492001, Chhattisgarh, India

Abstract


The paper is mainly concerned with the existence and uniqueness of solution for a class of Cauchy initial value problem of fractional order with impulses and infinite delay. The criteria on existences and uniqueness are obtained via successive approximation and solution operator. Finally an example is given to support our main result.

Keywords


Caputo Fractional Derivative, Existence and Uniqueness, Fractional Impulsive Differential Equation, Infinite Delay



DOI: https://doi.org/10.17485/ijst%2F2016%2Fv9i16%2F132680