Some qualitative properties of nonlinear fractional integro-differential equations of variable order

Ahmed Refice; Mohammed Said  Souid; Ali Yakar

doi:10.11121/ijocta.2021.1198

Authors

Ahmed Refice Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, Algeria https://orcid.org/0000-0002-8906-6211
Mohammed Said Souid Department of Economic Sciences, University of Tiaret, Algeria https://orcid.org/0000-0002-4342-5231
Ali Yakar Department of Mathematics, Gaziosmanpasa University, Tokat, Turkey https://orcid.org/0000-0003-1160-577X

DOI:

https://doi.org/10.11121/ijocta.2021.1198

Keywords:

Fractional differential equations of variable order, Boundary value problem, Fixed point theorem, Ulam-Hyers-Rassias stability

Abstract

The existence-uniqueness criteria of nonlinear fractional integro-differential equations of variable order with multiterm boundary value conditions are considered in this work. By utilizing the concepts of generalized intervals combined with the piecewise constant functions, we transform our problem into usual Caputo’s fractional differential equations of constant order. We develop the necessary criteria for assuring the solution's existence and uniqueness by applying Schauder and Banach fixed point theorem. We also examine the stability of the derived solution in the Ulam-Hyers-Rassias (UHR) sense and provide an example to demonstrate the credibility of the results.

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Author Biographies

Ahmed Refice, Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, Algeria

is a researcher from Djillali Liabes University of Sidi Bel-Abbes, Algeria

Mohammed Said Souid, Department of Economic Sciences, University of Tiaret, Algeria

is a professor at University of Tiaret, Algeria. He has many publications on existence and stability of fractional differential equations of variable order.

Ali Yakar, Department of Mathematics, Gaziosmanpasa University, Tokat, Turkey

received his Ph.D.degree in applied mathematics from Gebze Institute of Technology, Turkey in 2010. His primary interest is in investigating existence and uniqueness of fractional order differential equations. He is currently working as a professor at Department of Mathematics at Tokat Gaziosmanpaşa University.

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