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Article

Existence of Solutions for Nonlinear Fractional Differential Equations and Inclusions Depending on Lower-Order Fractional Derivatives

1
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore 641020, India
2
Department of Mathematics, Cankaya University, Balgat 06530, Ankara, Turkey
3
Institute of Space Science, 077125 Magurele-Bucharest, Romania
*
Author to whom correspondence should be addressed.
Axioms 2020, 9(2), 44; https://doi.org/10.3390/axioms9020044
Received: 23 March 2020 / Revised: 13 April 2020 / Accepted: 13 April 2020 / Published: 25 April 2020
(This article belongs to the Special Issue Fractional Calculus, Wavelets and Fractals)
This article deals with the solutions of the existence and uniqueness for a new class of boundary value problems (BVPs) involving nonlinear fractional differential equations (FDEs), inclusions, and boundary conditions involving the generalized fractional integral. The nonlinearity relies on the unknown function and its fractional derivatives in the lower order. We use fixed-point theorems with single-valued and multi-valued maps to obtain the desired results, through the support of illustrations, the main results are well explained. We also address some variants of the problem. View Full-Text
Keywords: single-valued map; multi-valued map; Caputo derivative; generalized Riemann–Liouville integral single-valued map; multi-valued map; Caputo derivative; generalized Riemann–Liouville integral
MDPI and ACS Style

Muthaiah, S.; Baleanu, D. Existence of Solutions for Nonlinear Fractional Differential Equations and Inclusions Depending on Lower-Order Fractional Derivatives. Axioms 2020, 9, 44. https://doi.org/10.3390/axioms9020044

AMA Style

Muthaiah S, Baleanu D. Existence of Solutions for Nonlinear Fractional Differential Equations and Inclusions Depending on Lower-Order Fractional Derivatives. Axioms. 2020; 9(2):44. https://doi.org/10.3390/axioms9020044

Chicago/Turabian Style

Muthaiah, Subramanian, and Dumitru Baleanu. 2020. "Existence of Solutions for Nonlinear Fractional Differential Equations and Inclusions Depending on Lower-Order Fractional Derivatives" Axioms 9, no. 2: 44. https://doi.org/10.3390/axioms9020044

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