A Study of Nonlinear Fractional q

This paper is concerned with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional q-difference equations with nonlocal integral boundary conditions. The existence results are obtained by applying some well-known fixed point theorems and illustrated with examples

Nonlinear qq-fractional differential equations with nonlocal and sub-strip type boundary conditions

This paper is concerned with new boundary value problems of nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions. Our results are new in the present setting and rely on the contraction mapping principle and a fixed point theorem due to O'Regan. Some illustrative examples are also presented

Existence results for nonlinear multi-term impulsive fractional q-integro-difference equations with nonlocal boundary conditions

This paper is concerned with the existence of solutions for a nonlinear multi-term impulsive fractional $q$-integro-difference equation with nonlocal boundary conditions. The appropriated fixed point theorems are applied to accomplish the existence and uniqueness results for the given problem. We demonstrate the application of the obtained results with the aid of examples

A Langevin-Type q-Variant System of Nonlinear Fractional Integro-Difference Equations with Nonlocal Boundary Conditions

We introduce a new class of boundary value problems consisting of a q-variant system of Langevin-type nonlinear coupled fractional integro-difference equations and nonlocal multipoint boundary conditions. We make use of standard fixed-point theorems to derive the existence and uniqueness results for the given problem. Illustrative examples for the obtained results are also presented

On Solvability of Fractional (<i>p</i>,<i>q</i>)-Difference Equations with (<i>p</i>,<i>q</i>)-Difference Anti-Periodic Boundary Conditions

We discuss the solvability of a (p,q)-difference equation of fractional order α∈(1,2], equipped with anti-periodic boundary conditions involving the first-order (p,q)-difference operator. The desired results are accomplished with the aid of standard fixed point theorems. Examples are presented for illustrating the obtained results

A Langevin-Type <i>q</i>-Variant System of Nonlinear Fractional Integro-Difference Equations with Nonlocal Boundary Conditions

We introduce a new class of boundary value problems consisting of a q-variant system of Langevin-type nonlinear coupled fractional integro-difference equations and nonlocal multipoint boundary conditions. We make use of standard fixed-point theorems to derive the existence and uniqueness results for the given problem. Illustrative examples for the obtained results are also presented

Existence Theory for q-Antiperiodic Boundary Value Problems of Sequential q-Fractional Integrodifferential Equations

We discuss the existence and uniqueness of solutions for a new class of sequential q-fractional integrodifferential equations with q-antiperiodic boundary conditions. Our results rely on the standard tools of fixed-point theory such as Krasnoselskii's fixed-point theorem, Leray-Schauder nonlinear alternative, and Banach's contraction principle. An illustrative example is also presented