Fractional Differential Equations
New Advancements for Generalized Fractional Derivatives
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Article
Functional delay random semilinear differential equations
In this paper, we study the existence of integral solutions of a functional differential equation with delay and random effects. We base our arguments on some suitable random fixed point theorem with stochasti...
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Article
A fixed point theorem for Proinov map**s with a contractive iterate
In this paper, we consider the fixed point theorem for Proinov map**s with a contractive iterate at a point. In other words, we combine and unify the basic approaches of Proinov and Sehgal in the framework o...
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Chapter
Introduction
Fractional calculus is a field in mathematical analysis which is a generalization of integer differential calculus that involves real or complex order derivatives and integrals [10–14, 25, 28, 43, 50–52]. Ther...
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Chapter
Preliminary Background
In this chapter, we discuss the necessary mathematical tools, notations, and concepts we need in the succeeding chapters. We look at some essential properties of fractional differential operators. We also revi...
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Chapter
Preliminary Background
This chapter discusses the mathematical tools, notations, and concepts that will be required in subsequent chapters.
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Chapter
Fractional Differential Equations with Instantaneous Impulses
The aim of this chapter is to prove some existence, , and -Hyers-Rassias stability results for a class of value problem for nonlinear fractional differential equations with and generalized -type fract...
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Fractional Differential Equations with Retardation and Anticipation
In this chapter, we some existence and results for a class of and terminal problems for nonlinear k-generalized \(\psi \) ψ - fractional differential equations involving both retarded and advanc...
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Chapter
Coupled Systems for Fractional Differential Equations
This chapter deals some existence and results for a class of coupled for nonlinear k-generalized \(\psi \) ψ -Hilfer fractional differential equations with boundary and terminal conditions. Our resul...
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Book
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Chapter
Introduction
Fractional calculus is an area of mathematical analysis that extends the concepts of integer differential calculus to involve real or complex order derivatives and integrals.
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Chapter
Implicit Fractional Differential Equations
This chapter deals with some existence and Ulam stability results for a class of initial and boundary value problems for differential equations with generalized Hilfer-type fractional derivative in Banach spaces.
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Chapter
Hybrid Fractional Differential Equations
This chapter is devoted to proving some results concerning the existence of solutions for a class of initial and boundary value problems for nonlinear fractional Hybrid differential equations and Generalized H...
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Chapter
Fractional Differential Equations with Non-Instantaneous Impulses
The present chapter deals with some existence, , and stability results for a class of initial and value problems for nonlinear fractional differential equations with non-instantaneous and generalized ...
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Impulsive Fractional Differential Equations with Retardation and Anticipation
This deals with the existence and results for a class of impulsive initial and value problems for nonlinear fractional differential equations and k-Generalized \(\psi \) ψ - fractional derivative i...
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Article
Open AccessExtended Proinov \({\mathfrak {X}}\) -contractions in metric spaces and fuzzy metric spaces satisfying the property \({{\mathcal {N}}}{{\mathcal {C}}}\) by avoiding the monotone condition
In recent years, Fixed Point Theory has achieved great importance within Nonlinear Analysis especially due to its interesting applications in real-world contexts. Its methodology is based on the comparison bet...
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Chapter
Introduction
Fixed point theory can be described as a framework for researching and investigating the existence of the solution of the equation \(f(p)=p\) ...
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Chapter
Metric Spaces
The notion of the metric can be considered as a generalization of two point distance that was contrived systematically first by Euclid. In the modern mathematical set-up, Maurice René Frechét [116] is the firs...
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Chapter
Generalization of Metric Spaces
In this chapter, we discuss some of the interesting generalizations and extensions of the notion of the metric. Roughly speaking, the notion of metric can be considered as an axiomatic form of the “distance”. ...
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Chapter
Metric Fixed Point Theory
The aim of this chapter is to give a brief history of metric fixed point theory. In this section, we discuss the pioneer metric fixed point theorem that was given by Banach [56]. This outstanding result is kno...
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Chapter
Fixed Point Theorems on b-Metric Spaces
In this chapter, we collect some important fixed point theorems. Fixed point theorems in b-metric spaces have been studied by many author, e.g. [11, 12, 20, 23, 36, 37, 45, 57, 59, 71, 72, 74, 76, 77, 79, 117, 11...
