Existence results of Hilfer integro-differential equations with fractional order

Ramasamy Subashini; Chokkalingam Ravichandran; Kasthurisamy Jothimani; Haci Mehmet Baskonus

doi:10.3934/dcdss.2020053

Article Contents

2020, Volume 13, Issue 3: 911-923. Doi: 10.3934/dcdss.2020053

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Existence results of Hilfer integro-differential equations with fractional order

1.
Department of Mathematics, GTN Arts College, Dindigul - 624 004, Tamil Nadu, India
2.
PG and Research Department of Mathematics, Kongunadu Arts and Science College(Autonomous), Coimbatore - 641 029, Tamil Nadu, India
3.
Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore - 641 202, Tamil Nadu, India
4.
Department of Mathematics, Faculty of Education, Harran University, Sanliurfa, Turkey

^* Corresponding author: H. M. Baskonus
^* Corresponding author: H. M. Baskonus

Received: June 30, 2018

Revised: August 31, 2018

Published: December 2019

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Abstract

The paper is relevance with Hilfer derivative with fractional order which is generalized case of R-L and Caputo's sense. We ensured the solution using noncompact measure and M$ \ddot{\text{o}} $nch's fixed point technique. Illustrative examples are included for the applicability of presented technique.

Keywords:

Mild solution,
Laplace transform,
MNC,
M$ \ddot{\text{o}} $nch's fixed point technique,
evolution equation.

Mathematics Subject Classification: 34A12, 46F12, 47H08, 47H10, 47J35.

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