Theory of Nonlinear Implicit Fractional Differential Equations

This paper deals with the basic theory of nonlinear implicit fractional differential equations involving Caputo fractional derivative. In particular, we investigate the existence and interval of existence of solutions, uniqueness, continuous dependence of solutions on initial conditions, estimates o...

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Published inDifferential equations and dynamical systems Vol. 28; no. 1; pp. 1 - 17
Main Authors Kucche, Kishor D., Nieto, Juan J., Venktesh, Venktesh
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.01.2020
Springer Nature B.V
Subjects
Computer Science
Dependence
Differential equations
Engineering
Initial conditions
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear equations
Original Research
approximate solution
Integral inequality
Fixed point theorem
39B12
Implicit fractional differential equations
34A12
26A33
Continuous dependence
Caputo fractional derivative
Existence and uniqueness
34A08
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Summary:This paper deals with the basic theory of nonlinear implicit fractional differential equations involving Caputo fractional derivative. In particular, we investigate the existence and interval of existence of solutions, uniqueness, continuous dependence of solutions on initial conditions, estimates on solutions and continuous dependence on parameters and functions involved in the equations. Further, we study ε -approximate solution of the implicit fractional differential equations.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-016-0297-7