Nonexistence results for nonlinear fractional differential inequalities involving weighted fractional derivatives

Andrea De Gaetano; Mohamed Jleli; Maria Alessandra Ragusa; Bessem Samet

doi:10.3934/dcdss.2022185

Article Contents

2023, Volume 16, Issue 6: 1300-1322. Doi: 10.3934/dcdss.2022185

This issue Previous Article Parametric Robin double phase problems with critical growth on the boundary Next Article Global existence, general decay and blow-up for a nonlinear wave equation with logarithmic source term and fractional boundary dissipation

Nonexistence results for nonlinear fractional differential inequalities involving weighted fractional derivatives

1.
National Research Council of Italy (CNR), CNR-IRIB and CNR-IASI, Palermo and Rome, Italy
2.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia
3.
Department of Mathematics and Computer Science, Catania University, 95125 Catania, Italy
4.
RUDN University, 6 Miklukho, Maklay St, Moscow 117198, Russia
5.
Dept. of Biomatics, Óbuda University, Budapest, Hungary

^*Corresponding author: Bessem Samet
^*Corresponding author: Bessem Samet

Received: May 2022

Early access: November 2022

Published: June 2023

Abstract / Introduction Full Text(HTML) Related Papers Cited by

Abstract

In this paper, we study the nonexistence of global solutions for certain classes of nonlinear fractional differential inequalities involving weighted fractional derivatives and a singular potential function. Namely, using the test function method with a judicious choice of the test function, we obtain sufficient criteria depending on the parameters of the considered problems, under which we have absence of global solutions. Next, some special cases of the potential function are discussed.

Keywords:

Mathematics Subject Classification: Primary: 34K37, 34A08; Secondary: 35B44.

Citation:

Full Text(HTML)

Related Papers

Cited by

References

[1]	K. Adolfsson and M. Enelund, Fractional derivative viscoelasticity at large deformations, Nonlinear Dyn., 33 (2003), 301-321. doi: 10.1023/A:1026003130033.
[2]	O. P. Agrawal, Generalized multiparameters fractional variational calculus, Int. J. Differ. Equ., 2012 (2012), Art. ID 521750, 38 pp. doi: 10.1155/2012/521750.
[3]	O. P. Agarwal, Some generalized fractional calculus operators and their applications in integral equations, Fract. Calc. Appl. Anal., 15 (2012), 700-711. doi: 10.2478/s13540-012-0047-7.
[4]	S. Buonocore and F. Semperlotti, Tomographic imaging of non-local media based on space-fractional diffusion models, J. Appl. Phys., 123 (2018), Article 214902.
[5]	K. M. Furati and M. Kirane, Necessary conditions for the existence of global solutions to systems of fractional differential equations, Fract. Calc. Appl. Anal., 11 (2008), 281-298.
[6]	M. D. Kassim, K. M. Furati and N.-E. Tatar, Nonexistence of global solutions for a fractional differential problem, J. Comput. Appl. Math., 314 (2017), 61-68. doi: 10.1016/j.cam.2016.10.006.
[7]	A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol 204, Elsevier, Amsterdam, The Netherlands, 2006.
[8]	M. Kirane and S. A. Malik, The profile of blowing-up solutions to a nonlinear system of fractional differential equations, Nonlinear Anal., 73 (2010), 3723-3736. doi: 10.1016/j.na.2010.06.088.
[9]	V. V. Kulish and J. L. Lage, Application of fractional calculus to fluid mechanics, J. Fluids Eng., 124 (2002), 803-806.
[10]	F. Mainardi, Fractional calculus in wave propagation problems, Forum der Berliner Mathematischer Gesellschaft, 19 (2011), 20-52.
[11]	E. Mitidieri and S. I. Pohozaev, A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities, Proc. Steklov Inst. Math., 234 (2001), 1-362.