Some Differential Inequalities for Boundary Value Problems of Fractional Integro-Differential Equations

Year 2022, Volume: 10 Issue: 2, 276 - 281, 31.10.2022

Hadi Kutlay Ali Yakar

Abstract

We consider fractional integro-differential equations with boundary conditions and prove some differential inequalities related to given problem with the aid of technique of upper and lower solutions. We require these theorems because they serve as the basis for improvement of monotone iterative technique to such type of differential equations of boundary value problems.

Keywords

Fractional differential equations, Differential inequalities, Upper and Lower solutions, Boundary Value Problem

References

• [1] Agarwal, R., Benchohra, M. & Hamani, S. A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Applicandae Mathematicae. 109, 973-1033 (2010)
• [2] Yakar, A. & Koksal, M. Existence results for solutions of nonlinear fractional differential equations. Abstract And Applied Analysis. 2012 (2012)
• [3] Refice, A., Souid, M. & Yakar, A. Some qualitative properties of nonlinear fractional integro-differential equations of variable order. An International Journal Of Optimization And Control: Theories & Applications (IJOCTA). 11, 68-78 (2021)
• [4] Guezane, L. & Ashyralyev, A. Existence of solutions for weighted p (t)-Laplacian mixed Caputo fractional differential equations at resonance. Filomat. 36, 231-241 (2022)
• [5] Gambo, Y., Ameen, R., Jarad, F. & Abdeljawad, T. Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives. Advances In Difference Equations. 2018, 1-13 (2018)
• [6] Singh, H., Kumar, D. & Baleanu, D. Methods of mathematical modelling: fractional differential equations. (CRC Press,2019)
• [7] Kazem, S. Exact solution of some linear fractional differential equations by Laplace transform. International Journal Of Nonlinear Science. 16, 3-11 (2013)
• [8] Devi, J. & Sreedhar, C. Generalized Monotone Iterative Method for Caputo Fractional Integro-differential Equation. European Journal Of Pure And Applied Mathematics. 9, 346-359 (2016)
• [9] Kilbas, A., Srivastava, H. & Trujillo, J. Theory and applications of fractional differential equations. (elsevier,2006)
• [10] Lakshmikantham, V., Leela, S. & Devi, J. Theory of fractional dynamic systems. (Cambridge Academic ,2009)
• [11] Lakshmikantham, V. & Vatsala, A. Theory of fractional differential inequalities and applications. Communications In Applied Analysis. 11, 395-402 (2007)
• [12] Al-Refai, M. & Luchko, Y. Comparison principles for solutions to the fractional differential inequalities with the general fractional derivatives and their applications. Journal Of Differential Equations. 319 pp. 312-324 (2022)
• [13] Yakar, A. & Kutlay, H. A note on comparison results for fractional differential equations. AIP Conference Proceedings. 1676, 020064 (2015)
• [14] Yakar, A. Some generalizations of comparison results for fractional differential equations. Computers & Mathematics With Applications. 62, 3215-3220 (2011)