A New Method for Investigating Approximate Solutions of Some Fractional Integro-Differential Equations Involving the Caputo-Fabrizio Derivative
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Abstract
We present a new method to investigate some fractional integro-differential equations involving the Caputo-Fabrizio derivation and we prove the existence of approximate solutions for these problems. We provide three examples to illustrate our main results. By checking those, one gets the possibility of using some discontinuous mappings as coefficients in the fractional integro-differential equations.
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Approximate Solution, Caputo-Fabrizio Derivative, Fractional Integro-Differential Equation, Generalized Alpha-Contractive Map, Generalized α-Contractive Map, Financial economics, First-order partial differential equation, Fractional Differential Equations, Economics, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Differential equation, Numerical Methods for Singularly Perturbed Problems, FOS: Mathematics, Functional Differential Equations, Anomalous Diffusion Modeling and Analysis, Numerical Analysis, Algebra and Number Theory, Integro-differential equation, Applied Mathematics, Fractional calculus, Partial differential equation, Applied mathematics, Fractional Derivatives, Modeling and Simulation, Derivative (finance), Physical Sciences, Fractional Calculus, Analysis, Mathematics, Ordinary differential equation, fractional integro-differential equation, Caputo-Fabrizio derivative, Fractional derivatives and integrals, Other nonlinear integral equations, generalized \(\alpha\)-contractive map, Functional-differential equations with fractional derivatives, approximate solution
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Baleanu, Dumitru; Mousalou, Asef; Rezapour, Shahram (2017). A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo-Fabrizio derivative, Advances in Difference Equations.
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111
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2017
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1
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