Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition
Date
2020
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Abstract
The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green’s function of the proposed problems. With the aid of a Green’s function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained. © 2020, The Author(s).
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Keywords
Anti-Periodic Condition, Pantograph Differential Equation, Φ-Caputo Fractional Derivative, Evolutionary biology, Pantograph differential equation, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Context (archaeology), Differential equation, Numerical Methods for Singularly Perturbed Problems, Φ-Caputo fractional derivative, QA1-939, FOS: Mathematics, Fixed-point theorem, Boundary value problem, Biology, Anomalous Diffusion Modeling and Analysis, Numerical Analysis, Banach space, Applied Mathematics, Fractional calculus, Paleontology, Partial differential equation, Applied mathematics, Function (biology), Modeling and Simulation, Physical Sciences, Anti-periodic condition, Uniqueness, Finite Difference Schemes, Mathematics, Ordinary differential equation, Nonlinear boundary value problems for ordinary differential equations, pantograph differential equation, Fractional derivatives and integrals, \(\Phi\)-Caputo fractional derivative, Applications of operator theory to differential and integral equations, anti-periodic condition, Periodic solutions to functional-differential equations, Functional-differential equations with fractional derivatives
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02 engineering and technology, 01 natural sciences, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics
Citation
Ahmed, Idris...et al. (2020). "Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition", Advances in Difference Equations, Vol. 2020, No. 1.
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OpenCitations Citation Count
8
Source
Advances in Difference Equations
Volume
2020
Issue
1
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CrossRef : 6
Scopus : 12
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