Picard–Lindelöf theorem ≈ Picard–Lindelöf theorem
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Existence and uniqueness of weak solutions for a class of fractional superdiffusion equations Open
In this paper, we consider the existence and uniqueness of weak solutions for a class of fractional superdiffusion equations with initial-boundary conditions. For a multidimensional fractional drift superdiffusion equation, we just conside…
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On orthogonal sets and Banach fixed point theorem Open
We introduce the notion of the orthogonal sets and give a real generalization of Banach' fixed point theorem.As an application, we find the existence of solution for a first-order ordinary differential equation.
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EXISTENCE THEOREMS AND HYERS-ULAM STABILITY FOR A CLASS OF HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS WITH P -LAPLACIAN OPERATOR Open
In this paper, we prove necessary conditions for existence and uniqueness of solution (EUS) as well Hyers-Ulam stability for a class of hybrid fractional differential equations (HFDEs) with p-Laplacian operator. For these aims, we take hel…
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Existence theorems and Hyers-Ulam stability for a coupled system of fractional differential equations with p-Laplacian operator Open
In this paper, we study the existence and uniqueness of solution (EUS) as well as Hyers-Ulam stability for a coupled system of FDEs in Caputo’s sense with nonlinear p-Laplacian operator. For this purpose, the suggested coupled system is tr…
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Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives Open
The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607–2619, 2017). Depending on the value of ρ in the li…
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Existence of Solutions for a Class of Coupled Fractional Differential Systems with Nonlocal Boundary Conditions Open
Applying Schauder fixed point theorem and Leray-Schauder nonlinear alternative theory, this paper is concerned with the existence of solutions to coupled fractional differential systems with fractional integral boundary value conditions. M…
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Existence and uniqueness of the solution to uncertain fractional differential equation Open
The paper proves an existence and uniqueness theorem of the solution to an uncertain fractional differential equation by Banach fixed point theorem under Lipschitz and linear growth conditions. Then, the paper presents an existence theorem…
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Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative Open
In this paper, the Hyers–Ulam stability of linear Caputo–Fabrizio fractional differential equation is established using the Laplace transform method. We also derive a generalized Hyers–Ulam stability result via the Gronwall inequality. In …
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Applications of measures of noncompactness to infinite system of fractional differential equations Open
In this paper, we discuss few existence result for solution of an infinite system of fractional differential equations of order ?(1 < ? < 2), with three point boundary value problem in the interval [0, T]. The problem is studied in the cla…
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Existence and Uniqueness of Solutions for Fractional Neutral Volterra-Fredholm Integro Differential Equations Open
The topic fractional calculus can be measured as an old as well as a new subject. In the fractional calculus the various integral inequalities plays an important role in the study of qualitative and quantitative properties of solution of d…
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Ordinary Differential Equations Open
In this chapter, we discuss a first application of the time derivative operator constructed in the previous chapter. More precisely, we analyse well-posedness of ordinary differential equations and will at the same time provide a Hilbert s…
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Existence and stability of impulsive coupled system of fractional integrodifferential equations Open
In this manuscript, we deal with a class and coupled system of implicit fractional differential equations, having some initial and impulsive conditions. Existence and uniqueness results are obtained by means of Banach’s contraction mapping…
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Multi-Strip and Multi-Point Boundary Conditions for Fractional Langevin Equation Open
In the present paper, we discuss a new boundary value problem for the nonlinear Langevin equation involving two distinct fractional derivative orders with multi-point and multi-nonlocal integral conditions. The fixed point theorems for Sch…
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Some New Generalization of Darbo’s Fixed Point Theorem and Its Application on Integral Equations Open
In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point th…
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On existence theorems for some generalized nonlinear functional-integral equations with applications Open
In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and funct…
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Application of measures of noncompactness to the infinite system of second-order differential equations in ℓ p $\ell_{p}$ spaces Open
In this article, we use the technique based upon measures of noncompactness in conjunction with a Darbo-type fixed point theorem with a view to studying the existence of solutions of infinite systems of second-order differential equations …
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Existence theory and stability analysis to a system of boundary value problem Open
The aims and objectives of this manuscript are devoted to investigate some adequate results for the existence of solution to a nonlinear coupled system of fractional order differential equations (FDEs). Appropriate conditions for the exist…
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Fractional partial random differential equations with infinite delay Open
The present paper deals with some existence results for the Darboux problem of partial fractional random differential equations with infinite delay. The arguments are based on a random fixed point theorem with stochastic domain combined wi…
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Ulam Type Stability for a Coupled System of Boundary Value Problems of Nonlinear Fractional Differential Equations Open
We discuss existence, uniqueness, and Hyers-Ulam stability of solutions for coupled nonlinear fractional order differential equations (FODEs) with boundary conditions. Using generalized metric space, we obtain some relaxed conditions for u…
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A Proof of the Bloch Theorem for Lattice Models Open
The Bloch theorem is a powerful theorem stating that the expectation value of the U(1) current operator averaged over the entire space vanishes in large quantum systems. The theorem applies to the ground state and to the thermal equilibriu…
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Existence, Uniqueness and Ulam’s Stability of Solutions for a Coupled System of Fractional Differential Equations with Integral Boundary Conditions Open
In this paper, the existence and uniqueness of the solutions to a fractional order nonlinear coupled system with integral boundary conditions is investigated. Furthermore, Ulam’s type stability of the proposed coupled system is studied. Ba…
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A Simple Proof and Strengthening of a Uniqueness Theorem for L-functions Open
We give a simple proof and strengthening of a uniqueness theorem for functions in the extended Selberg class.
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Existence of Solutions for Nonlocal Boundary Value Problem of Hadamard Fractional Differential Equations Open
We investigate the existence and uniqueness of solutions for Hadamard fractional differential equations with non-local integral boundary conditions, by using the Leray Schauder nonlinear alternative, Leray Schauder degree theory, Krasnosel…
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Stability of Ulam–Hyers and Ulam–Hyers–Rassias for a class of fractional differential equations Open
In this paper, we investigate a class of nonlinear fractional differential equations with integral boundary condition. By means of Krasnosel’skiĭ fixed point theorem and contraction mapping principle we prove the existence and uniqueness o…
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On a nonlocal boundary value problem for nonlinear second-order Hahn difference equation with two different q , ω $q,\omega$ -derivatives Open
In this paper, we study a nonlocal boundary value problem for a second-order Hahn difference equation. Our problem contains two Hahn difference operators with different numbers of q and ω. An existence and uniqueness result is proved by us…
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Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations Open
We study the existence, uniqueness, and various kinds of Ulam–Hyers stability of the solutions to a nonlinear implicit type dynamical problem of impulsive fractional differential equations with nonlocal boundary conditions involving Caputo…
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Fractional-order boundary value problems with Katugampola fractional integral conditions Open
In this paper, we study existence (uniqueness) of solutions for nonlinear fractional differential equations with Katugampola fractional integral conditions. Several fixed point theorems are used for sufficient conditions of existence (uniq…
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Existence and uniqueness of solutions for system of Hilfer–Hadamard sequential fractional differential equations with two point boundary conditions Open
In this paper, we study existence and uniqueness of solutions for a system of Hilfer–Hadamard sequential fractional differential equations via standard fixed point theorems. The existence is proved by using the Leray–Schauder alternative, …
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On the Existence and Uniqueness of Solutions for Local Fractional Differential Equations Open
In this manuscript, we prove the existence and uniqueness of solutions for local fractional differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using the contracting mapping theorem (CMT) and increasing an…
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Solutions of fractional differential equations with p-Laplacian operator in Banach spaces Open
In this paper, we study the solutions for nonlinear fractional differential equations with p-Laplacian operator nonlocal boundary value problem in a Banach space. By means of the technique of the properties of the Kuratowski noncompactness…