New Existence Results on R-L Fractional Derivative under Weak Topology Attribute

Authors

  • Ananthi Kantheeban Department of Mathematics, Sree Sowdambika College of Engineering, Aruppukotai-626 134, Tamilnadu, India
  • D Swathi Department of Mathematics, Sree Sowdambika College of Engineering, Aruppukotai-626 134, Tamilnadu, India
  • U Karthik Raja Research Centre and PG Department of Mathematics, The Madura College, Madurai - 625 011, Tamilnadu, India
  • Kamal Shah Department of Mathematics University of Malakand
  • Thabet Abdeljawad Department of Mathematics and Sciences, Prince Sultan University , Riyadh 11586, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i1.6932

Keywords:

Fractional calculus; Volterra integral; Nemytskii’s; weak topology; Existence; Fixed point.

Abstract

In this article, the research examines whether Riemann-Liouville-type fractional derivatives can be used to solve an initial value problem under weak topology conditions. As a way to prove the existence of integrable description and a new type of iteration of a Leray–Schauder nonlinear alternative for the weak topology, it will be demonstrated, and the given problem is first transformed into the sum of two integral operators, and then the modified version of Krasnoselskii’s fixed point hypothesis in weak topology is employed. Finally, an example is given to illustrate the effectiveness of our main findings.

Author Biographies

  • Ananthi Kantheeban, Department of Mathematics, Sree Sowdambika College of Engineering, Aruppukotai-626 134, Tamilnadu, India

    Researcher inDepartment of Mathematics, Sree Sowdambika College of Engineering, Aruppukotai-626 134, Tamilnadu, India

  • D Swathi, Department of Mathematics, Sree Sowdambika College of Engineering, Aruppukotai-626 134, Tamilnadu, India

    Researcher in Department of Mathematics, Sree Sowdambika College of Engineering, Aruppukotai-626 134, Tamilnadu, India

  • U Karthik Raja, Research Centre and PG Department of Mathematics, The Madura College, Madurai - 625 011, Tamilnadu, India

    Teacher at Research Centre and PG Department of Mathematics, The Madura College, Madurai - 625 011, Tamilnadu, India

  • Thabet Abdeljawad, Department of Mathematics and Sciences, Prince Sultan University , Riyadh 11586, Saudi Arabia

    Professor in Department of Mathematics and Sciences, Prince Sultan University , Riyadh 11586, Saudi Arabia

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Published

2026-02-16

Issue

Vol. 19 No. 1: (January 2026)

Section

Differential Equations

License

Copyright (c) 2026 Ananthi Kantheeban, D Swathi, U Karthik Raja, Kamal Shah, Thabet Abdeljawad

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How to Cite

New Existence Results on R-L Fractional Derivative under Weak Topology Attribute. (2026). European Journal of Pure and Applied Mathematics, 19(1), 6932. https://doi.org/10.29020/nybg.ejpam.v19i1.6932