Unified existence results for nonlinear fractional boundary value problems-Reference-Cited by-同舟云学术

Unified existence results for nonlinear fractional boundary value problems

Published:2024 Issue:2 Volume:9 Page:4118-4134
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Talib Imran¹,Batool Asmat²,Riaz Muhammad Bilal³⁴,Alam Md. Nur⁵

Affiliation:

1. Department of Mathematics, Nonlinear Analysis Group (NAG), Virtual University of Pakistan, 54-Lawrence Road, Lahore, Pakistan

2. Department of Mathematics, University of Management and Technology, 54770 Lahore, Pakistan

3. IT4Innovations, VSB - Technical University of Ostrava, Ostrava, Czech Republic

4. Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon

5. Department of Mathematics, Pabna Unversity of science and Technology, Pabna-6600, Bangladesh

Abstract

<abstract><p>In this work, we focus on investigating the existence of solutions to nonlinear fractional boundary value problems (FBVPs) with generalized nonlinear boundary conditions. By extending the framework of the technique based on well-ordered coupled lower and upper solutions, we guarantee the existence of solutions in a sector defined by these solutions. One notable aspect of our study is that the proposed approach unifies the existence results for the problems that have previously been discussed separately in the literature. To substantiate these findings, we have added three illustrative examples.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference25 articles.

1. A. Gerasimov, A generalization of linear laws of deformation and its application to problems of internal friction, Akad. Nauk SSSR. Prikl. Mat. Meh, 12 (1948), 251–260.

2. G. Scott-Blair, The role of psychophysics in rheology, Journal of Colloid Science, 2 (1947), 21–32. http://dx.doi.org/10.1016/0095-8522(47)90007-X

3. A. Kilbas, H. Srivastava, J. Trujillo, Theory and applications of fractional differential equations, North-Holland: Elsevier, 2006.

4. I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, San Diego: Elsevier, 1999. http://dx.doi.org/10.1016/s0076-5392(99)x8001-5

5. M. Benchohra, E. Karapinar, J. Lazreg, A. Salim, Advanced topics in fractional differential equations: a fixed point approach, Cham: Springer, 2023. http://dx.doi.org/10.1007/978-3-031-26928-8

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